Robotic apparatus

ABSTRACT

A robotic apparatus has eight actuators (M 0 -M 7 ) and a linkage (LINK  0 -LINK  5 ) that actuates an end effector. Three serial macro freedoms have large ranges of motion and inertias. Four serial micro freedoms have small ranges of motion and inertias. Translation of the end effector in an y direction is actuated by at least one micro joint and at least one macro joint. The apparatus can be part of a master and slave combination, providing force feedback without any explicit force sensors. The slave is controlled with an Inverse Jacobian controller, and the mater with a Jacobian Transpose controller. A slave having more degrees of freedom (DOFs) than the master can be controlled. A removable effector unit actuates its DOFs with cables. Beating heart surgery can be accomplished by commanding the slave to move with a beating heart and cancelling out any such motion in the motions perceived by the master.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a divisional of and claims the benefit of priorityfrom U.S. patent application Ser. No. 10/893,613 (Attorney Docket No.017516-005521US), filed Jul. 15, 2004; which is a divisional ofapplication Ser. No. 09/508,871 (Attorney Docket No. 017516-005520US),filed Jul. 17, 2000; which is a 35 U.S.C. §371 United States NationalStage application of International Patent Application No.PCT/US98/19508, filed on Sep. 18, 1998; which claims priority to U.S.Provisional Application No. 60/059,395, filed on Sep. 19, 1997; the fulldisclosures of which are incorporated herein by reference.

The inventions disclosed herein are also somewhat related to inventionsby two of the inventors herein (Salisbury and Madhani), described inthree U.S. patent applications, all of which are incorporated herein byreference. The three applications were all filed on May 16, 1997, asfollows: ARTICULATED SURGICAL INSTRUMENT FOR PERFORMING MINIMALLYINVASIVE SURGERY WITH ENHANCED DEXTERITY AND SENSITIVITY, U.S. Ser. No.08/857,776, issued Aug. 11, 1998, as U.S. Pat. No. 5,792,135;FORCE-REFLECTING SURGICAL INSTRUMENT AND POSITIONING MECHANISM FORPERFORMING MINIMALLY INVASIVE SURGERY WITH ENHANCED DEXTERITY ANDSENSITIVITY, U.S. Ser. No. 08/858,048; and WRIST MECHANISM FOR SURGICALINSTRUMENT FOR PERFORMING MINIMALLY INVASIVE SURGERY WITH ENHANCEDDEXTERITY AND SENSITIVITY, U.S. Ser. No. 08/857,655, issued Aug. 25,1998 as U.S. Pat. No. 5,797,900. Each of these, in turn, claimedpriority to Provisional application No. 60/017,981, filed May 20, 1996,which is herein incorporated by reference.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY SPONSOREDRESEARCH OR DEVELOPMENT

The United States Government has certain rights in this inventionpursuant to the DARPA program under Contract No. DAMD194-c-4123.

BACKGROUND OF THE INVENTION

Minimally invasive surgery (“MIS”) techniques reduce the amount ofextraneous tissue that are damaged during diagnostic or surgicalprocedures, thereby reducing patient recovery time, discomfort, anddeleterious side effects. It is estimated that 7,000,000 surgeriesperformed each year in the United States can be performed in a minimallyinvasive manner. However, only about 1,000,000 of the surgeriescurrently use these techniques, due to limitations in minimally invasivesurgical instruments and techniques and the additional training requiredto master them.

Advances in minimally invasive surgical technology could have a dramaticimpact. The average length of a hospital stay for a standard surgery is8 days, while the average length for the equivalent minimally invasivesurgery is 4 days. Thus the complete adoption of minimally invasivetechniques could save 24,000,000 hospital days, and billions of dollarsannually in hospital residency costs alone. Patient recovery times,patient discomfort, surgical side effects, and time away from work arealso reduced with minimally invasive surgery.

The most common form of minimally invasive surgery is endoscopy. Acommon form of endoscopy is laparoscopy, which is minimally-invasiveinspection and surgery inside the abdominal cavity. In standardlaparoscopic surgery, a patient's abdomen is insufflated with gas, andcannula sleeves are passed through small (approximately ½ inch {1 cm.))incisions to provide entry ports for laparoscopic surgical instruments.

The laparoscopic surgical instruments generally include a laparoscopefor viewing the surgical field, and working tools, such as clamps,graspers, scissors, staplers, and needle holders. The working tools aresimilar to those used in conventional (open) surgery, except that theworking end of each tool is separated from its handle by anapproximately 12-inch long extension tube.

To perform surgical procedures, the surgeon passes instruments throughthe cannula and manipulates them inside the abdomen by sliding them inand out through the cannula., rotating them in the cannula, levering(i.e., pivoting) the instruments in the abdominal wall and actuating endeffectors on the distal end of the instruments. The instruments pivotaround centers of rotation approximately defined by the incisions in themuscles of the abdominal wall. The surgeon observes the procedure by atelevision monitor, which displays the abdominal worksite image providedby the laparoscopic camera.

Similar endoscopic techniques are employed in arthroscopy,retroperitoneoscopy, pelviscopy, nephroscopy, cystoscopy, cistemoscopy,sinoscopy, hysteroscopy and urethroscopy. The common feature of all ofthese minimally invasive surgical techniques is that they generate animage of a worksite within the human body and pass specially designedsurgical instruments through natural orifices or small incisions to theworksite to manipulate human tissues and organs, thus avoiding thecollateral trauma caused to surrounding tissues, which would result fromcreating open surgical access.

There are many disadvantages of current minimally invasive surgicaltechnology. First, the video image of the worksite is typically atwo-dimensional video image displayed on an upright monitor somewhere inthe operating room. The surgeon is deprived of three-dimensional depthcues and may have difficulty correlating hand movements with the motionsof the tools displayed on the video image. Second, the instruments pivotat the point where they penetrate the body wall, causing the tip of theinstrument to move in the opposite direction to the surgeon's hand.Third, existing MIS instruments deny the surgeon the flexibility of toolplacement found in open surgery. Most laparoscopic tools have rigidshafts and are constrained to approach the worksite from the directionof the small incision. Those that include any articulation have onlylimited maneuverability. Fourth, the length and construction of manyendoscopic instruments reduces the surgeon's ability to feel forcesexerted by tissues and organs on the end effector of the tool.

Overcoming these disadvantages and achieving expertise in endoscopicprocedures requires extensive practice and constant familiarization withendoscopic tools. However, despite surgeons' adaptation to thelimitations of endoscopic surgery, the technique has brought with it anincrease in some complications seldom seen in open surgery, such asbowel perforations due to trocar or cautery injuries. Moreover, one ofthe biggest impediments to the expansion of minimally invasive medicalpractice remains lack of dexterity of the surgical tools and thedifficulty of using the tools.

In a tangentially related area, telesurgery systems are being developedto increase a surgeon's dexterity as well as to allow a surgeon tooperate on a patient from a remote location. “Telesurgery” is a generalterm for surgical systems where the surgeon indirectly controls surgicalinstrument movements rather than directly holding and moving the tools.In a system for telesurgery, the surgeon is provided with an image ofthe patient's body at the remote location. While viewing thethree-dimensional image, the surgeon manipulates a master device, whichcontrols the motion of a servomechanism-actuated slave instrument, whichperforms the surgical procedures on the patient. The surgeon's hands andthe master device are positioned relative to the image of the operationsite in the same orientation as the slave instrument is positionedrelative to the act. During the operation, the slave instrument providesmechanical actuation and control of a variety of surgical instruments,such as tissue graspers, needle drivers, etc., which each performvarious functions for the surgeon, i.e., holding or driving a needle,grasping a blood vessel or dissecting tissue.

Such telesurgery systems have been proposed for both open and endoscopicprocedures. An overview of the state of the art with respect totelesurgery technology can be found in “Computer Integrated Surgery:Technology and Clinical Applications” (MIT Press, 1996). Prior systemsfor telesurgery are also described in U.S. Pat. Nos. 5,417,210,5,402,801, 5,397,323, 5,445,166, 5,279,309 and 5,299,288.

Proposed methods of performing telesurgery using telemanipulators alsocreate many new challenges. One is presenting position, force, andtactile sensations from the surgical instrument back to the surgeon'shands as he/she operates the telesurgery system, such that the surgeonhas the same feeling as if manipulating the surgical instrumentsdirectly by hand. For example, when the instrument engages a tissuestructure, bone, or organ within the patient, the system should becapable of detecting the reaction force against the instrument andtransmitting that force to the surgeon. Providing the instrument withforce reflection helps reduce the likelihood of accidentally damagingtissue in areas surrounding the operation site. Force reflection enablesthe surgeon to feel resistance to movements of the instrument when theinstrument engages tissue. A system's ability to provide forcereflection is limited by factors such as friction within the mechanisms,gravity, the inertia of the surgical instrument and the size of forcesexerted on the instrument at the surgical incision. Even when forcesensors are used, inertia, friction and compliance between the motorsand force sensors decreases the quality of force reflection provided tothe surgeon.

Another challenge is that, to enable effective telesurgery, theinstrument must be highly responsive and must be able to accuratelyfollow the rapid hand movements that a surgeon may use in performingsurgical procedures. To achieve this rapid responsive performance, asurgical servomechanism system must be designed to have an appropriatelyhigh servo bandwidth. This requires that the instrument have lowinertia. It is also preferable if the system can enhance the dexterityof the surgeon compared to standard endoscopic techniques by providingmore degrees-of-freedom (“DOFs”) to perform the surgery by means of aneasily controlled mechanism. By more DOFs, it is meant more joints ofarticulation, to provide more flexibility in placing the tool end point.

Another challenge is that to enable minimally invasive surgery, theinstrument must be small and compact in order to pass through a smallincision. Typically MIS procedures are performed through cannulasranging from 5 mm. to 12 mm. in diameter.

Surgeons commonly use many different tools (sometimes referred to hereinas end-effectors) during the course of an operation, including tissuegraspers, needle drivers, scalpels, clamps, scissors, staplers, etc. Insome cases, it is necessary for the surgeon to be able to switch,relatively quickly, from one type of end effector to another. It is alsobeneficial that effectors be interchangeable (even if not very quickly),to reduce the cost of a device, by using the portion of the device thatdoes not include the end effector for more than one task.

However, the mass and configuration of the effector affects the dynamicsand kinematics of the entire system. In typical cases, the effector iscounter balanced by other elements of the system. Thus, to the extentthat effectors are interchangeable, this interchangeability featureshould be accomplished without rendering the remainder of the systemoverly complicated.

What is needed, therefore, is a servomechanical surgical apparatus forholding and manipulating human tissue under control of a teleoperatorsystem.

It would also be desirable to provide a servomechanical surgicalapparatus that can provide the surgeon with sensitive feedback of forcesexerted on the surgical instrument.

It would further be desirable to provide a servomechanical surgicalapparatus that is highly responsive, has a large range of motion and canaccurately follow rapid hand motions that a surgeon frequently uses inperforming surgical procedures.

It would still further be desirable to provide a servomechanicalsurgical apparatus that increases the dexterity with which a surgeon canperform endoscopic surgery, such as by providing an easily controlledwrist joint.

It would also be desirable to provide a dexterous surgical apparatushaving a wrist with three independent translational degrees-of-freedom,which can provide force feedback with respect to those three degrees offreedom.

It would still further be desirable to provide a surgical instrumenthaving a wrist mechanism for minimally invasive surgery, which issuitable for operation in a telemanipulator mechanism.

It would additionally be desirable to provide a servomechanical surgicalapparatus that has easily interchangeable end effectors, the exchange ofwhich does not require significant adjustments to the kinematic anddynamic control of the apparatus, thereby allowing different endeffectors to be used on one base unit, either during the same operation,or, at least, during different operations.

To some extent, the inventions discussed in the three patentapplications by the present inventors Madhani and Salisbury that areincorporated herein by reference, address these goals. The inventiondescribed herein further satisfies these goals.

BRIEF SUMMARY OF THE INVENTION

A preferred embodiment of the invention is a robotic apparatuscomprising: seven actuators, M0, M1, M2, M3, M4, M5 and M6; a support;an end effector link having an effector reference point; and a linkageof links and joints between the support and the end effector linkreference point. The linkage comprises: three macro joints, coupled toeach other in series, one of which joint 0 is coupled directly to thesupport, the joints operating to provide three macro translation DOFs tothe end effector link reference point, which macro DOFs arecharacterized by a relatively large range of motion; and four additionaljoints, designated micro joints coupled in series with the three macrojoints and coupled to each other in series, one of which micro joints,joint 6 being coupled directly to the end effector link reference point,the four micro joints operating to provide three micro translation DOFsto the end effector link reference point, which micro DOFs arecharacterized by a relatively small range of motion as compared to themacro DOFs and where the micro DOFs are redundant with the macro DOFswith respect to translation. For each of the actuators, there is atransmission, coupled to the actuator and coupled to at least one of theseven (four micro plus three macro) joints, thereby actuating each ofthe seven joints.

The actuators are mounted such that during translation of the effectorlink reference point, the actuators move through no more than two macroDOFs, and such that they move through no micro DOFs. The linkagecomprises macro links that are movable only with the macro DOFs, andother, micro links that are movable through both the macro DOFs and themicro DOFs. The micro links each have a relatively low inertia, ascompared to the inertia of any one of the macro links.

According to another preferred embodiment, the three macro jointscomprise: a joint 0, a rotary joint about an axis A0, coupled to thesupport and to a joint 0 link; joint 1, a rotary joint, about an axisA1, orthogonal to the axis A0 and coupled to the joint 0 link and to ajoint 1 link; and joint 2, a translational joint along an axis A2,spaced from and perpendicular to the axis A1 and coupled to the joint 1link and to a joint 2 link.

According to yet another preferred embodiment, the four micro jointscomprise: joint 3, a rotary joint about an axis A3, that is parallel tothe Axis A2, coupled to the joint 2 link and to an elongated hollowshaft link; joint 4, a rotary joint about an axis A4, that isperpendicular to the axis A3, coupled to the hollow shaft link and to anextension link; joint 5, a rotary joint about an axis A5, that is spacedfrom and parallel to the axis A4, coupled to the extension link and toan effector support link; and joint 6, a rotary joint about an axis A6that is spaced from and perpendicular to the axis A5, coupled to theeffector support link and to the end effector link.

There may also be an eighth actuator M7 and an additional joint, whichcouples an end effector jaw link to the effector support link, to rotatearound an axis A7, which jaw link is operable to move toward and awayfrom the end effector link, thereby effectuating gripping of an objecttherebetween.

According to still another preferred embodiment, a total of six effectorcable tension segments extend from various components of the endeffector, through the elongated hollow link.

A preferred embodiment of a micro macro manipulator as described abovealso includes a controller that controls the manipulator according to anInverse Jacobian controller, where the gains of the macro freedoms areadjusted to be much larger than the gains of the micro freedoms, on theorder of the ratio of the inertias thereof.

According to a related preferred embodiment, the transmission comprisesthe six cables and a base set of transmission elements, which are eachcoupled directly to one of the actuators; and a releasable couple, whichcouples an individual one of the six effector cable tension segments toan individual one of the base set of transmission elements. The basetransmission elements may include cable segments.

According to still another preferred embodiment, any one of theembodiments of the invention outlined above may constitute a slaveactuator unit. A master actuator unit may be provided, having a masterlinkage, having: a master reference point, coupled to a master groundsupport through a plurality of master links and master joints; and aplurality of master actuators, coupled to the master linkage to actuatethe master reference point. A controller is coupled to the slave unitactuators, configured to control the slave according to an InverseJacobian controller. Another controller is coupled to the masteractuators, configured to control the master according to a JacobianTranspose controller.

The macro freedom gains and the micro freedom gains are preferablychosen such that the inertia of the macro freedoms is suppressed in anyforces felt at the master reference point.

According to yet another preferred embodiment, the slave unit linkage ischaracterized by a number X of DOFs, X being at least seven DOFs and themaster unit linkage is characterized by a number Y of DOFs where Y is atleast one fewer than X. According to this embodiment, the slavecontroller can be configured to resolve a redundancy in control due tothe difference between the X DOFs of the slave unit and the fewer Y DOFsof the master unit by applying a cost function to a range of possiblejoint configurations, each of which provide the same location of the endeffector link reference point, and minimizing the cost function.

Another preferred embodiment of the invention is a robotic apparatushaving a base unit and an effector unit. The base unit has a support, anactuator M0 and a base linkage, connected to the support, and to theeffector unit. The base linkage comprises a drivable member D0, drivableby the actuator M0 through a DOF DOF0, such that the effector end of thebase linkage is drivable through the DOF0. The base linkage alsoincludes a drivable member D1, movable through the DOF0 with thedrivable member D0, and also through another DOF DOF1. An actuator M1,drives the drivable member D1 through the DOF1, such that the effectorend of the linkage is drivable through the DOF1. An actuator set, whichis drivable with the drivable member D1 through the DOF1, comprises aplurality of K actuators. Each of the plurality K has one terminalthereof fixed relative to the drivable member D1, and one terminalthereof free to move through one DOF relative to the drivable member D1.The base further includes a plurality K of base transmission elements,each of the plurality K coupled with a free terminal of one of the Kactuators, and each of the base transmission elements including aneffector transmission coupling site. This base, alone, is a preferredembodiment of the invention. It can also be used, in combination withthe effector unit, described as follows.

The effector unit has a base end, connected to the base linkage, an endeffector and an effector linkage comprising a plurality of links andjoints, which effector linkage extends from the base end to the endeffector. For each joint, an effector transmission element is connectedto a link that is adjacent the joint and that also has a base couplingsite distant from the link connection. For each effector transmissionelement, a transmission clamp connects the effector transmission elementto a corresponding base transmission element, thereby coupling theeffector transmission element, and thereby its associated link, to amovable terminal of one of the plurality K of actuators.

According to such a preferred embodiment, the end effector has N=K+2DOFs under action of the plurality K actuators and the two actuators M0and M1, none of which plurality K actuators are movable through any ofthe N DOFs other than the DOF0 and DOF1.

The end effector just described may also be used with other types ofbase supports. A releasable couple between the transmission elements ofthe base and the effector completes the transmission.

It is also a preferred embodiment of the invention to provide, coupledto the Inverse Jacobian controller and to the Jacobian Transposecontroller, an environment position sensor, arranged to generate asignal that corresponds to the translational position of a referencepoint in an environment in which the slave may reside. The InverseJacobian controller further commands the macro freedom actuators andmicro freedom actuators to move the effector reference point in concertwith the environment reference point. The Jacobian Transpose controllerfurther is configured to command the master to move the master referencepoint to follow only motion of the effector reference point that doesnot correspond to motion of the environment reference point. Thispresents the effect to a user who is in contact with the masterreference point that the effector is interacting with an environmentthat is substantially motionless. Thus, a surgeon engaging the mastercan use the slave to operate on a beating heart, while perceiving theheart as stationary.

According to yet another preferred embodiment of the invention, at leasttwo base transmission elements of a base, such as is described above,comprise cables and at least two corresponding effector transmissionelements comprise cables. An extent of the at least two basetransmission elements extend substantially parallel to each other and anextent of the at least two effector transmission elements extendsubstantially parallel to each other. The extent of each of the at leasttwo effector transmission elements that extends substantially parallelto each other is parallel to and adjacent to the extent of thecorresponding of the at least two base transmission elements thatextends substantially parallel to each other. The adjacent extents ofcorresponding effector and base transmission elements can be clamped toeach other such that motion of the base transmission elements istransmitted to the effector transmission elements. There can be anynumber of pairs of cables so clamped to each other.

Yet another preferred embodiment of the invention is simply a couplebetween an actuator unit and an effector unit of a robotic apparatus.The actuator unit, comprises an actuator that actuates a tension bearingtransmission element, comprising a tension segment that is arranged tofollow a straight line for a portion of its path [PAS]. The effectorunit comprises a movable end effector link, coupled to a tension bearingtransmission element, comprising a tension segment that is arranged tofollow a straight line for a portion of its path PES, which PES isarranged parallel to the portion PAS. A releasable couple clamps theportion PAS of the actuator unit transmission element to the portion PESof the effector unit transmission element, thereby releasably couplingthe actuator to the end effector link. There can be a large number ofparallel transmission elements so linked together, for instance at leastsix.

Still another preferred embodiment of the invention is An actuator setcomprising a plurality of actuators, each actuator having a first and asecond terminal, the second of which is rotatable about an output axisrelative to the first, which second terminal is adapted to engage atransmission element, each of the output axes having a component thereofthat is parallel. For each of the actuators, a transmission element islooped around the rotatable terminal, forming two tension segments. Foreach of the transmission elements there are a pair of low frictioncircular surfaces, along each of which passes one of the two tensionsegments. The pair of circular surfaces are centered about an axis thatis substantially perpendicular to a component of the output axis of therespective actuator. There is also turnaround located along the path ofthe transmission element between the points at which it engages eachpulley of the pair, such that tension is maintained on the transmissionelement. The axes of the actuators may be parallel.

Yet another preferred embodiment of the invention is a method ofcontrolling a manipulator, as described above, comprising the steps of:coupling a controller to the manipulator actuators; configuring thecontroller to control the manipulator according to an Inverse Jacobiancontroller; commanding the micro freedom actuators M3, M4, M5 and M6with micro freedom gains; and commanding the macro freedom actuators M0,M1 and M2 with macro freedom gains that are much larger than the microfreedom gains.

The method may further include sizing the macro and micro freedom gainssuch that the ratio of a representative one of the micro freedom gainsto a representative one of the macro freedom gains is on the order of aratio of a representative one of the micro freedom inertias to arepresentative one of the macro freedom inertias.

A preferred embodiment of the invention also includes controlling such amanipulator as a slave apparatus, by a master apparatus, including thefurther step of configuring a Jacobian Transpose controller to commandthe master to move the master reference point to follow motion of theeffector reference point.

A final preferred embodiment of the invention is a method of controllingsuch a manipulator, when the slave unit linkage is characterized by anumber X of DOFs, X being at least seven DOFs and the master unitlinkage is characterized by a number Y of DOFs where Y is at least onefewer than X, the method further comprising the step of resolving aredundancy in control due to the difference between the X DOFs of theslave unit and the fewer Y DOFs of the master unit by applying a costfunction to a range of possible joint configurations, each of whichprovide the same location of the end effector link reference point, andminimizing the cost function.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features, aspects, and advantages of the presentinvention will become better understood with regard to the followingdescription, appended claims and accompanying drawings, where:

FIG. 1 is a schematic representation in a perspective view of anembodiment of a base positioning unit and wrist unit of the invention;

FIG. 2 is a schematic representation in a perspective view of thekinematics of the embodiment of a base positioning unit and wrist unitof the invention shown in FIG. 1, showing the joint orientations in anominal “zero” position;

FIG. 3 is a schematic representation in a side view of the kinematics ofthe embodiment of a base positioning unit and wrist unit of theinvention shown in FIG. 1, showing how a remote center is established;

FIG. 4 is a schematic representation in a side view of the embodiment ofthe base positioning unit and wrist unit of the invention shown in FIG.1, showing its range of motion pitching forward 60° around axis 1;

FIG. 5 is a schematic representation in a side view of the embodiment ofthe base positioning unit and wrist unit of the invention shown in FIG.1, showing its range of motion pitching backward 60° around axis 1;

FIG. 6 is a schematic representation showing the workspace of theembodiment of the invention shown in FIG. 1;

FIG. 7A is a schematic representation in a perspective view of link 1,the motor block, of a preferred embodiment of the base unit of theinvention;

FIG. 7B is a schematic representation in an end view of the motors of anembodiment of the invention that actuate the wrist DOFs, showing therouting of the cables from the motors to adjacent pulleys;

FIG. 7C is a schematic representation in a perspective view, of thegraduated pulleys shown in FIG. 7B, generally from the opposite end;

FIG. 8 is a schematic representation in a perspective view of the weightthat is housed in the motor block, of a preferred embodiment of the baseunit of the invention;

FIG. 9 is a schematic representation in a side view of the embodiment ofthe base positioning unit and wrist unit of the invention shown in FIG.1, showing the cabling for the base unit;

FIG. 10 is a schematic representation in a perspective view of theembodiment of the link 5 of the base positioning unit and the carriagethat rides thereon to connect with the wrist unit of the invention shownin FIG. 1;

FIG. 11 is a schematic representation in a perspective view of theembodiment of the wrist unit of the invention shown in FIG. 1;

FIG. 12 is a schematic representation in a perspective view of a fivejoint wrist of the embodiment of the wrist unit of the invention shownin FIG. 1;

FIG. 13 is a schematic representation showing a preferred embodiment ofthe interface between the six cables that actuate the wrist and twelveof the cables that emanate from the motors;

FIG. 14 is a schematic representation showing three different positionsthat the wrist of the invention shown in FIG. 12 can assume;

FIG. 15 is a schematic representation showing a position in which thewrist of the invention shown in FIG. 12 can be placed, which position issingular;

FIG. 16 shows schematically the wrist cabling for an embodiment of thewrist of the invention shown in FIG. 12;

FIG. 17 shows schematically the wrist cabling for rotation of wristjoint 3 about axis 3, for an embodiment of the wrist of the inventionshown in FIG. 12;

FIG. 18 shows schematically the portion of the wrist cabling distantfrom the wrist joints, for an embodiment of the wrist of the inventionshown in FIG. 12;

FIG. 19 is a schematic representation showing a side view of a portionof the base unit and the wrist unit of a preferred embodiment of theinvention, showing the connection between a wrist cable and itscorresponding base drive cable;

FIG. 20 is a schematic representation showing a perspective view of amaster unit of a preferred embodiment of the invention;

FIG. 21 is a schematic representation showing the kinematics of a masterunit of a preferred embodiment of the invention shown in FIG. 20;

FIG. 22A is a schematic representation in block diagram form showing aknown Jacobian transpose position-derivative control scheme for a masterand a slave;

FIG. 22B is a schematic representation in block diagram form showing anInverse Jacobian position derivative controller for a slave, with aJacobian transpose position derivative controller for a master, for thecontrol of a slave having X DOFs by a master having Y DOFs, where X isgreater than Y, which can also implement a macro-micro control scheme;

FIG. 23 is a schematic representation of a one DOF master and slaveapparatus to illustrate macro-micro control;

FIG. 24A is a graph showing the position along the z axis of the masterand the slave in a freespace test of a macro-micro control scheme forthe embodiment of the invention shown in FIG. 1, with the solid linerepresenting the master and the dashed line representing the slave;

FIG. 24B is a graph showing the force at the master and the slave in thefreespace test of a macro-micro control illustrated in FIG. 24A;

FIG. 25A is a graph showing the position along the z axis of the masterand the slave in a contact test of a macro-micro control scheme for theembodiment of the invention shown in FIG. 1, with the solid linerepresenting the master and the dashed line representing the slave;

FIG. 25B is a graph showing the force at the master and the slave in thecontact test of a macro-micro control illustrated in FIG. 25A;

DETAILED DESCRIPTION OF THE INVENTION Mechanism Overview

The following is an overview of the system. More details are provided insubsequent sections. A preferred embodiment of a slave apparatus of theinvention is shown in FIG. 1 and consists of two main subsystems, a baseunit 302 and a wrist unit 304. The base unit contains all of theactuators M0-M7 for the entire system, the links link 0-link 5 andprovides a mechanical interconnect 306 for the wrist unit 304, whichwrist is a passive (i.e. contains no actuators) detachable instrument.The following components are referred to in FIG. 1, and the kinematicstructure, including axis and link numbers, is defined in the schematicdrawing FIG. 2. Eight joints are labeled 0-7. (The links are notnecessarily associated with respectively numbered axes.) The system isgrounded through a ‘U″-shaped stationary base bracket’ 308. A spindlelink 0, rotates within this base about axis 0. Motor M0 actuates thisaxis 0 using a cable drive connected to the axis 0 drive drum. Link 1rotates about axis 1 within the spindle. Link 1 holds motors M1-M7.

Motor M1 drives Link 1 about axis 1 using a cable drive similar to thatused for axis 0, connected to the axis 1 drive drum. A difference isthat the axis 0 drive drum rotates relative to the axis 0, while theaxis 1 drive drum is stationary relative to the axis 1. The othermotors, M1-M7, are all mounted within link 1. Remote center kinematics(discussed below) are formed by the links 1-5. Links 1, 3, and 5 are themain structural members, while links 2 and 4 act in tension andcompression. Link 5 holds two bearing rails 306 on which a carriage 310rides. The carriage 310 holds the wrist unit 304, which comprises amechanical attachment (not shown in FIG. 1), an instrument shaft 312,and an end effector 314 consisting of a wrist 316 and grippers 318, inthe embodiment shown.

Remote Center Kinematics

The purpose of the base positioner 302 is to position the wrist unit 304with two degrees-of-freedom (‘DOF”) (pitch and yaw) inside the humanbody, without violating the constraint imposed by the fixed tissueincision point. Combined with a translational degree of freedom alongthe tool shaft 312, which is part of the wrist unit, this provides threetranslational DOF positioning (e.g. x,y,z) for the wrist 316 and fingersor jaws 318. These three DOFs are without regard to DOFs provided byactuation of the wrist itself 314 relative to the tool shaft 316. Thekinematics that accomplish this are shown in FIG. 3. The doubleparallelogram linkage shown gives the instrument shaft two rotary DOFsabout a remote center point 111. One DOF is rotation about the axis 0,which rotation is into and out of the page, indicated at arrow 57. Theother DOF is rotation about axis 1 for the parallelogram and about axis1 _(R) for the tool shaft 312, indicated by the arcs α and α_(R),respectively, and the arrow 56.

Offsets in the links (from the placement shown in FIG. 3) allowplacement of the carriage and link 5 behind the remote center (towardsthe base) in order to give room for the wrist unit. (See FIG. 9.)

Range of Motion and Workspace

The embodiment of the invention shown in FIG. 1 can pitch forwards andbackwards about axis 1 by ±60 degrees, as shown in FIGS. 4 (forward) and5 (backward) respectively. As discussed below, the motors are placedsuch that they form a “V” shape, which straddles link 3, facilitating alarger rearward pitch angle than would be possible with anotherconfiguration, while still allowing the weight of the motors to beplaced where it can counterbalance the system. It can also yaw aboutaxis 0 by +80 degrees. Soft stops 320, 322 made from aluminum coveredwith soft foam rubber in these two main base axes provides safety.

The overall workspace is portion of a hemisphere with a central, smallspherical portion and two conical portions removed, as shown in FIG. 6.The flat surfaces are inclined with respect to each other (in theinstance shown at 1600) and they extend 1200 between their straightedges. The distance between the spherical surfaces is defined as the“stroke”. The location of the truncating spherical surfaces depends onthe length of the instrument 312. For example, if the instrument shaft312 is shorter, access can be had nearer to the remote center 111. Thevolume of the workspace is generated by rotating the flat surface shownaround the y axis (as shown in FIG. 6) through 1600. A typicalembodiment of the invention has a stroke along axis 2 of 20 cm (8 in)(with the illustrated type of the wrist unit), and a total carriagetravel of 25.4 an (10 in). The area near the remote center 111 cannot beeffectively used however with the wrist 314 shown in FIG. 1, because themanipulator is singular there. The illustrated wrist unit uses a 38 cm(15 in) instrument shaft, which can operate from 3.8 cm (1.5 in) to 24cm (9.5 in) from the remote center. Other wrists can, however, accessthis area near to the remote center, if desired.

Structure

A preferred embodiment of the structure should be relatively rigid. Forexample, a typical link 3 is two in (5 cm) aluminum square box tubingmachined to 0.050 in (0.13 cm) wall thickness. The pivot forks 324, 326,at the end of link 3 are welded, to minimize flexing that might be foundin bolted connections. This link 3 beam is 23 in (58.4 cm) long withpivots connecting it to links 1 and 2 at a distance of 5.5 in (14 cm)apart. Link 5 is 1 in×1.5 in (2.54 an X 3.8 cm) aluminum square tubingmachined to 0.050 (0.13 cm) in wall thickness.

As shown in FIG. 7A, link 1 includes a single “V” shaped aluminum block328, which houses the seven motors M1-M7, with two aluminum uprights330, 332, bolted to it. The cable idler pulleys 334, shown in FIG. 1,are mounted to a plate 336 that braces the two uprights 330, 332, acrosstheir backs to add structural stiffness. The top of the “V”, on the facethat is not shown in FIG. 7A, is open, to allow a portion of link 3 tofit between the arms of the “V” when the positioning device is in itsmost rearward configuration. The motors are in a “V” configuration whichfit around link 3 when the system is rotated rearwards.

The stiffness of a representative base structure 302 has been determinedby measuring the force required to deflect the end of link 3 by ⅛ in.(0.32 cm.) with the base held fixed (i.e., with no rotation about axes 0and 1). It was difficult to measure any deflection in the x direction.Because of the small distances over which forces could be applied,accuracy of these values is only about 20%.

k _(BY)≅5500 N/m

k _(BZ)≅12,000 N/m  (1)

Humans cannot distinguish a stiffness of 25,000 N/m from infiniterigidity, so 25,000 N/m is ideally the stiffness one might hope toachieve for the overall system, including structural stiffness and servostiffness of the slave and master. However, practically, a totalstiffness on the order of 2,000 N/m would be adequate.

Base Actuators

The base axes of a typical embodiment of the slave device of theinvention are powered by motors M0 and M1. Suitable motors are Maxonbrand brushed D.C. servomotors (RE035-071-034) with 4.8:1 planetarygearheads. (As used herein, the freedoms of the system are sometimesreferred to as ‘axes’ and sometimes as ‘joint.’ The terms are generallyinterchangeable, as used herein.) Additional cable and drum reductionadds approximately 29× reduction to give a total reduction of 137.92:1for joint 0 and 137.41:1 for joint 1. (The slight difference is causedby manufacturing tolerance.)

It is important that the servo response of the base axes 0 and 1 not beunderdamped, which can arise due to a lack of encoder resolution andinsufficient speed reduction. A preferred embodiment of the inventionwas designed such that the base actuator rotor inertias were roughlymatched to the output load inertia. That is:

$\begin{matrix}{R \cong {\sqrt{\frac{I_{{axis}\; 0}}{I_{rotor}}} \cdot}} & (2)\end{matrix}$

The inertia about axis 0 varies as axis 1 is moved through itsworkspace, so it is impossible to match these inertias in allconfigurations. Using a ProE (Parametric Technology Corporation,Waltham, Mass.) model of the system, the inertia of the system was foundabout joint 0 when link 5 is vertical (aligned with the z axis), notincluding motor inertia, to be 0.183 kgm². When the system is pitchedrearward by 60°, the inertia is 0.051 kgm². The motor rotor inertia is6.96×10⁻⁶ kgm². Using these two values, the reductions required to matchthe link and rotor inertias at these two configurations are:

$\begin{matrix}\begin{matrix}{R = {\sqrt{\frac{0.183}{6.96 \times 10^{- 6}}} = 162}} \\{R = {\sqrt{\frac{0.051}{6.96 \times 10^{- 6}}} = 86}}\end{matrix} & (3)\end{matrix}$

Wrist Actuators

FIG. 7A shows link 1, which houses motors M1-M7. The end effectoractuators are all placed within link 1. The same Maxon RE-035-071-034brushed D.C. motors with Canon brand TR36 laser encoders were used.These encoders have 14400 counts per revolution (after quadrature).

Each of the six motors M2-M7 that drive the wrist unit axes is mountedwith a threaded drive capstan e.g. 338. The capstan has a flexure clampmanufactured into it to clamp it to the motor shaft. Flats 340 andscrews 342 at each end of the clamp allow the cable to be terminated onthe pinion at each end. The cable is then wound towards the center ofthe pinion from each end in opposite directions and comes off of thepinion at essentially the same location along the length of the pinion.In this way, slippage on the pinion is impossible, and the extra lengthrequired to maintain frictional wraps on the pinion is eliminated. Thecable used on these axes is 0.024 in. (0.06 cm.) diameter 7×19construction, stainless-steel cable (Sava Industries, Riverdale, N.J.).

Threading the pinions prevents the cable from rubbing on itself as ittravels over the capstans. Also, the threads are semicircular incross-section so that the cable deforms minimally as it rolls onto andoff of the capstans. This is again to minimize friction generated withinthe cable itself.

The motors M2-M7 are placed parallel to one another. This is veryconvenient, as discussed below, and allows all the drive cables toemanate from the rear of link 1. This works very well with the basecabling scheme, which will be described below.

The motors M1-M7 nearly gravitationally counterbalance the slaveapparatus for a typical wrist unit 304. To complete and tune thecounterbalancing, an additional copper weight (in this case, of 0.95 kg(2.1 lbs)) is placed inside the opening 344 in link 1. The weight can bemoved forwards and backwards (generally along the x axis) for tuning.Further, it can be changed to another weight. The weight 346, shown inFIG. 8, incorporates water cooling passages 350 to cool the motor block320 in link 1. Since the motor block is a single piece of aluminum andcovers the entire length of the motors, it provides a good heat sink,and can be cooled using the copper counterweight. The copper weight 350is removable. If the wrist unit 304 is changed, the counterweight 350can also be easily changed to another weight that matches the mass ofthe replacement wrist.

The Maxon motors use a rotor, which consists of a wire basket set inepoxy. While this gives a low mechanical inertia, it also gives a lowthermal inertia, making the motors prone to overheating. By watercooling the motors, a factor of four improvement in the thermal powerdissipation can be achieved. At stall, this corresponds purely to l²Rlosses in the rotor and therefore gives a factor of two improvement inmaximum continuous torque output.

Base Cabling

The cabling for each of the six motors M2-M7 lies roughly parallel toeach other along links 1, 3 and 5. Each of these motors drives a singlecable loop 358. FIG. 9 shows how this works for a representative motorM, that is fixed to link 1. The solid lines represent mechanical cablesand the dashed lines represent the structural links. The loop begins byanchoring on the motor pinion at point A. The cable continues upwards,passing over the pulley P1 and under pulley P3. It continues along thelink 3 along axis x and passes under pulley P5, along link 5, overpulley P7, and is brought leftward along axis x around pulley P8. Itthen returns around other pulleys that lie next to the pulleys itoriginally passed around, pulleys P6, P4, P2, respectively and finallyterminating on the motor pinion at point B. The latter identifiedpulleys P6, P4, and P2, are not strictly visible in FIG. 9, beinglocated behind their mates, along they axis. Pulleys P3 and P4 lie alonga shaft 352, which forms the pivot between links 1 and 3, and pulleys P5and P6 lie on the shaft 354, which forms the pivot between links 3 and5. The shafts of pulleys P7 and P8 are fixed relative to each other butcan translate together along link 5 in order to tension the cable loop.Pulleys P1 and P2 ride on a shaft 356 a, which is fixed to link 1.Finally, the motor M is also fixed to link 1. An important feature ofthis cabling scheme is that as the system pitches forward and backwardabout axis 1, there is no length change in this cable loop and nocoupling between this pitching motion and the motor rotation.

As shown schematically in FIG. 7A, the motors M2-M7 are arranged withtheir axes substantially parallel. The route between these parallelmotor shafts to the idler pulleys 334 is shown from an end view in FIG.7B. Each motor is associated with a single cable loop, which has twotension elements, Cb_(dn), and Cb_(m), where the subscript d indicatesthat the cable is the drive portion that is connected to an associatedwrist cable (see FIG. 13) and then most closely encounters pulley P7,and the subscript r indicates that the cable is the return portion thatmost closely encounters pulley P8, and is not connected to an associatedwrist cable. The subscripts n (running from 2 to 7) correspond to themotor with which the cable is associated. (Only One Cable Pair isShown.)

As shown in FIG. 7B, the motors are spread out along the x and z axessuch that the cables associated with each can each pass over acorresponding pulley P1 for the drive tension elements and P2 for thereturn tension elements. There is one P1 pulley for each motor, and oneP2 pulley for each motor. The motors are grouped symmetrically in setsof three motors, with the six pulleys for each set of three motors beingcarried on a single shaft 356 a for the motors M2-M4; and 356 b for theremaining motors M5-M7.

The pulley shafts 356 a and 356 b are each inclined relative to the xaxis, such that the bottoms of all of the pulleys carried by each liealong a horizontal line (indicated by the dashed line h for the shaft356 a). As shown also in FIG. 7C, the pulleys P1 and P2 are of graduatedsizes, such that for each shaft 356 a and 356 b, the P1 pulley on theoutside (farthest from each other) has the largest diameter, and the P2pulley on the inside (nearest to each other) has the smallest diameter,and that all of the intermediate pulleys have intermediate diameters.The inclining of the shafts 356 a, (and the graduation of the pulleydiameters) is to minimize any angle of incidence between the cables andtheir respective pulleys. This is to reduce friction therebetween. Thegoal is to have the cables approaching the pulleys substantially in theplane that is defined by the pulley, at the pulley's middle.

To drive the wrist unit, a direct attachment is made between one side ofthe cable loop 358 and a cable of the wrist unit, between pulleys P5 andP7. This is further described below, after first describing the carriageand wrist unit.

Carriage

The carriage 310 for a typical embodiment of the invention, is shown inFIG. 10. The translational joint 2, along axis 2 is effected bytranslation of the carriage along rails, relative to link 5. Thecarriage runs on two 4 no stainless steel rails, each mounted in squareslots machined into a side of link 5 as bearing ways. Four rollerbearings 362, mounted on studs 364, ride on the steel rails 360. Two ofthe four studs are eccentric so that the bearings may be preloadedagainst the steel rails. The bearings themselves are shielded, so thatdirt and dust do not interfere with rolling of the balls within them,and lubricant is retained. The curvature between the bearing outer racesmatches the rails to reduce contact stresses. Each of the four bearings362 has a dynamic load capacity of 269 lbs. The aluminum tubing thatcomprises link 5 (the carriage beam) is machined from 1×1.5×⅛ in.(2.54×3.8×1.32 cm.) wall aluminum extrusion and is exceedingly stiff intorsion and in bending.

A flexure clamp 366 holds the body 368 of the wrist unit 304 to thecarriage. Cables run parallel to each other through a space S betweenthe clamp 366 and the carriage 310, as shown in FIG. 5. (Only a singlecable is shown in FIG. 5.) All cables lie substantially in the sameplane. Finally, the carriage beam link 5 has a support 370 at its bottomto support the slender wrist shaft 312. The support 370 incorporates aTeflon bushing to reduce friction.

Wrist Unit

The wrist unit 304 is shown separately in FIG. 11. It is a separateassembly that can be detached from the base unit 302. The cables, Cw₂,CW₃, . . . , CW₇, which drive the wrist, are shown schematically in FIG.13 and form closed pretensioned loops within the wrist unit 304. Asshown in FIGS. 13 and 19, the cables are mechanically attached to therespective base unit cables Cb_(d2)-Cb_(d7), when the wrist unit 304 ismounted onto the base unit 302. This attachment may be made using screwclamps 372. Using screw clamps, it takes several minutes to make theattachment. However, a quick-release capability is also desirable, andhardware that is capable of such quick-release is contemplated as partof the invention.

Wrist Kinematics

FIG. 12 shows a five joint (counting rotation around axis 3) wrist thatenables the use of macro-micro control (described below) with the baseunit 302, for 3 independent translational DOF of a reference point onthe end effector, e.g. the tip of finger 318 a. It is possible to use awrist unit having fewer or greater than five joints with the base unit302 if desired. (For instance, the four joint wrist shown in U.S. Pat.No. 5,792,135, mentioned above, may be used.) The wrist 314 isessentially a roll-pitch-pitch-yaw wrist, with the roll being about axis3, along the instrument shaft 312. The joint axes are labeled in FIG. 2,a portion of which is a kinematic diagram for the wrist shown in FIG.12.

As shown in FIG. 2, each joint is labeled numerically. Joint 2 is atranslational joint, effected by motion of the carriage 310 along itsrails, which translates the shaft 312 of the wrist unit 304 along axis2. Motion through this DOF from a nominal zero position (describedbelow) is indicated as q₂. The first rotary joint of the wrist, joint 3,rolls the entire wrist 314 around axis 3, which is coincident with axis2. The position of joint 3 is indicated by the angular displacement q₃.The next rotary joint is a first pitch joint, joint 4, which causespitching of the remaining portion (joints 5, 6 and 7) of the wrist unit304 about the axis 4, through an angular displacement q₃. Joint 4supports an extension link 380, which extends to the next rotary jointjoint 5. Joint 5 is a second pitch joint which causes pitching of theremaining portion (joints 6 and 7) of the wrist unit 304 about the axis5, which is always parallel to the axis 4, through an angulardisplacement q₄. Joint 5 directly supports an effector support link 382,which is connected to joints 6 and 7 through an effector axle 384. Thenext rotary joint is a yaw joint, joint 6, which yaws one finger 318_(b) of a two finger unit around the axis 6, which is alwaysperpendicular to axes 4 and 5. The angular displacement of a point thatis midway between this first finger and the second finger, from the homeposition is designated with q₆. The final rotary joint is also a sort ofyaw joint, joint 7, which yaws the other finger 318 _(a) of the twofinger unit around the axis 7, which is coincident with the axis 6. Theopening angle between the second finger and the first finger isdesignated q₇. The two fingers can be moved together, or separately. Ifthey are moved together, q, is considered to be zero.

All joint angles are defined relative to their respective proximal linkcloser to ground, except for joint 5, which is defined relative to axis3. The zero configuration is shown in FIG. 2 with all angles equal tozero.

As will be discussed below, to implement macro-micro control, thecombination of the base unit 302 and the wrist unit 304 must allowredundant macro and micro translations of a point on the end effectorin, ideally, each of three independent orthogonal directions, that is,any direction. By “redundant translation in a direction” it is meantthat for any configuration of the joints, there will be at least twojoints that can accommodate translation in that direction. Redundancy ineach of three independent orthogonal directions means that there willalways be two such joints no matter in what direction translation isdesired. Macro-micro redundancy means that of the two joints thatprovide for the translation, one is a micro joint and one is a macrojoint.

If redundant motion is provided for in only two independent directions,(for instance if there were no joint 5) there would always be onedirection (in that case, pointing directly into the fingers) whereredundancy did not exist, which would result in poor force reflection inthat direction. For instance, forces could not be felt along a line thatpasses through the finger tips and through axes 6/7 and which isperpendicular to that axis. The five joint wrist 314 of the inventionavoids that problem by having an extra pitch degree of freedom andmaintaining a right-angle bend in q5 (see FIG. 14) while reorienting.

FIG. 14 shows a number of different orientations that the wrist 314 canassume. A redundant degree of freedom, (joints 4 and 5) is maintainedcorresponding to motions directly into (i.e., stubbing) the fingers.(This is not a macro and micro redundancy. The macro redundancy would beprovided by at least one of joints 0, 1 and 2, depending on the jointconfiguration.)

Such a wrist also presents some challenges. As compared to a wristwithout joint 5, the wrist 314 has a kink in it. There is typically alimited amount of space at the surgical site and the extra room thatthis wrist occupies in certain configurations may not be available inall circumstances. Further, the wrist has essentially the samesingularities as does a roll-pitch-yaw wrist. For example, a singularconfiguration from which the wrist could not be moved occurs when thewrist pitch is at π/2, (q₅=λ/2) measured from the zero position shown inFIG. 2, as shown in FIG. 15.

Wrist Cabling and Mechanism

FIG. 16 shows a schematic diagram of the cabling scheme for the wrist314 shown in FIG. 12, for joints 2, 4, 5, 6 and 7. Cabling for rotaryjoint 3 is not shown in FIG. 16, but is shown in FIG. 17.

End Portion

The wrist is a roll-pitch-pitch-yaw wrist, where the joint 3 is theroll, joints 4 and 5 are the pitch joints, —joint 6 is the yaw and joint7 is an open/close around the yaw axis. Both the fingers rotate aboutaxes 6 and 7 as described below.

The wrist 314 is mounted to a hollow aluminum instrument shaft, 312,mounted along axis 3, through which six cables, CW₃, CW₃, CW₄, CW₅, CW₆and Cw₇ pass.

One of the objectives in designing a wrist is to keep the diameter ofpulleys within the wrist as large as possible, where the upper limitwill be the diameter of the instrument shaft. There are two reasons forthis. First, cable, and especially metal, e.g., steel cable, has aminimum bending radius, about which it may turn, since repeated bendingstresses in the cable will cause fatigue and failure in the individualcable fibers. The second reason is that there may be substantialfriction caused by pulling cable over a small radius. The motion ofcable fibers relative to each other increases as the pulley diameterdecreases, while at the same time cable tension is distributed over asmaller area. Under load this internal rubbing of the individual cablefibers represents energy loss and manifests itself as friction in theoverall drive. Although an embodiment of the invention is describedherein using polymeric cables, there may be situations where the addedstrength of metal cables is beneficial.

The fingers may be serrated, designed to hold needles. Alternatively,they could be made as retractors, microforceps, dissecting scissors,blades, etc.

Wrist Cabling

An N+1 cabling scheme (driving N freedoms with N+1 cables) is used in aportion of the wrist 314. The cable layout is shown schematically inFIG. 16. A portion of the cable layout is shown less schematically, butalso less completely in FIG. 18. The three joints: fingers 318 a and 318b, and pitch joint 5, are driven by four cables Cw₄, Cw₅, Cw₆, and Cw₇.These four cables represent the minimum number of tension elementsneeded to actuate three freedoms. Due to the particular unusualarrangement of axes and cables in the wrist of the invention shown, itis also possible to provide translation of these joints along thetranslational axis 2, by pulling on all four of the cables Cw₄, Cw₅,Cw₆, and Cw₇ at once. This is not typical of an N+1 system.

The cables that actuate rotational motion about the instrument shaft312, about axis 3, are omitted from FIG. 16, in order to more easilyshow cables Cw₃-Cw₇. The rotation results only in twisting of the cablesCw₃-Cw₇ inside the long instrument shaft tube 312. Due to the length ofthe instrument shaft 312, however, the resulting change in length of thecables is slight, and the length of the cables is long, so that theresulting resistance to rotational motion is on the order of the bearingfriction in joint 3, and substantially less than the torque due to brushfriction in the motor that drives this rotation (M2). This twisting ofthe cables does, however, limit rotation of the instrument shaft 312 tot 180°, at which point the cables will rub on each other, creatingfriction and wear.

As shown in FIG. 16, cables CW₇ and Cw₆ form two sides of a continuouscable loop. Cable CW₇ engages a proximal idler pulley 80, firstintermediate idler pulley 70, a second intermediate idler pulley 71, anddriven capstan 18 a. The cable loop returns from the driven capstan 18 aas cable Cw₆ and engages third and fourth intermediate idler pulleys 76and 77, and proximal idler pulley 80.

The cable CW₇ is coupled through a clamp 372 to one of the base cablesCb_(d7 (4,5,6 or 7)) that is driven by one of the motors M4, 5, 6 or 7between the idler pulleys 80 and 71. These four motors together actuatethe four joints 2, 5, 6 and 7, and it is arbitrary which motor isattached to which wrist cable. The cable Cw₆ is coupled through a clamp372 to another of the base drive cables Cb_(d (4,5,6 or 7)) that isdriven by the motors M4, 5, 6 or 7 between the idler pulleys 80 and 77.

Cables Cw₅ and Cw₄ form two sides of another continuous loop of cable.Cable Cw₅ engages a proximal idler pulley 78, the intermediate idlerpulleys 72 and 73 and driven capstan 18 b. The second cable loop returnsfrom the driven capstan 18 b as cable Cw₄ and engages intermediate idlerpulley 74, and 75 returning to and the proximal idler pulley 78.

The cable Cw₅ is coupled through a clamp 372 to another of the basecables Cb_(d(4, 5, 6 or 7)) that is driven by the motors M4, 5, 6 or 7between the idler pulleys 78 and 73. The cable Cw₄ is coupled through aclamp 372 to another one of the base cables Cb_(d(4, 5, 6 or 7)) that isdriven by the motors MA, 5, 6 or 7 between the idler pulleys 78 and 75.

The cable Cw₃ is coupled to joint 4. This cable has two tensionsections, Cw₃ and Cw₃, only one of which is coupled directly to a motor.As such, it is not part of an N+1 configuration, but represents insteada 2N configuration. This cable and this joint are connected to basecable Cb_(d3).

FIG. 17 shows a schematic of the cable Cw₂ used to drive joint 3,rotation about the axis 3. This cable is also shown in phantom on theright side of FIG. 18. The instrument shaft 312 is mounted to the drivencapstan 374 (not shown in FIG. 18), so that they rotate together. Thecable Cw₂ is clamped by a clamp 372 to a base cable Cb_(d2), which isdriven by the motor M2.

The idler pulleys 78 and 80 are located in the top 374 of the wrist unit304, shown in FIG. 18. They are tensioned by cable C_(T) which is fixedkinematically to the center of proximal idler pulleys 78 and 80. Thepulleys 78 and 80 ride on shafts (not shown) held in small forks intowhich the cables terminate. Each pulley uses a single ball bearing. Thecable C_(T), engages proximal idler pulley 82. Pulley 82 rides on ashaft held in a fork. This fork is mounted via a tensioning mechanism tothe bracket 102, which allows turning of a screw in order to tension thecables. The cables are arranged so that this single tensioning pointtensions all cables Cw₂-Cw₇.

The use of idler pulleys 78, 80, and 82 is unusual in N+1 cablingschemes. Typically, a separate motor is used for each of the N+1 cables.Using an extra motor has the advantage that the overall pretension inthe system is actively adjustable, which is useful when using arelatively high friction transmission, such as cable conduits. Howeverthe disadvantages are that an extra motor is required, and tension islost when motor power is turned off. This results in an unraveling ofcables at the driving capstan where multiple wraps are used to drive thecable. A pretensioned N+1 arrangement is much more convenient, whilemaintaining the advantage of minimizing cables which must pass throughthe shaft into the wrist and simplifying the wrist design.

The movement of the wrist and fingers is caused by coordinated motion ofthe motors. If motors M4 and M7 both act in concert, such that the cablearound the capstan 18 a is urged in the same direction, e.g. clockwise,as shown, by both motors, then finger 318 a will rotate. Similarly ifmotors M5 and M6 act in concert, finger 318 b will rotate. Theseseparate rotations, acting against each other provide gripping. Ifmotors M5 and M6 act in opposition, such that they pull the cable aroundthe capstan 18 a in opposite directions (thereby pulling cables Cw₄ andCw₅ to cause the cables to move in the same directions as each other,e.g. clockwise, around pulleys 74 and 72), and motors M4 and M7 act inopposition to each other, and also act relative to M5 and M6, such thatthe cables Cw₆ and Cw₇ are caused to move around the pulleys 76, and 70in the same direction as cables Cw₄ and Cw₅ move around pulleys 74 and72, then the wrist will pitch about axis 5. Finally, if all motors M4,M5, M6 and M7 act such that they pull the cables around the capstans 18a and 18 b in the same direction, e.g. to the right, as shown in FIG.16, the entire wrist unit will translate along axis 2. The exactdifferential transformations for the wrist described below, are givenbelow.

As shown in FIG. 16, the cables for the joints 5, 6, and 7 pass throughjoint 4 on idler pulleys 71, 73, 75, and 77. Two of the six cables thatpass through the instrument shaft actuate joint 4 (making up the loopthat includes the cable Cw₃ and Cw₃.). Joint 4 is actuated by motion ofmotor M3 alone. Rotation around axis 3 is actuated by motion of motor M2alone, as shown in FIG. 17.

In some cases, the use of alpha wraps within the wrist (e.g. at joint 4,around pulley 71) adds a considerable amount of friction. A wrist can bedesigned such that there are no alpha wraps. However this comes at acost of increasing the number of pulleys in the wrist and lengtheningthe wrist. If the four joint wrist shown in FIG. 12 were cabled weredesigned to avoid alpha wraps, eight additional pulleys would be needed,which would consume a considerable amount of space and add offsets tothe kinematic structure. To minimize the added friction but still use analpha-wrap design, non-metallic cable can be used, in particular Spectratype fiber in the form of Spiderwire™ fishing line, available fromJohnson Worldwide Associates, Sturtevant, Wis. This material is not asstiff as stainless steel cable, but it is smaller in diameter and ismuch smoother on its outside surface. As a result, as the cable slideson itself, as is inevitable in an alpha wrap, very little friction isadded.

The use of ballbearings was avoided in a preferred embodiment of thewrist unit. This makes sterilization easier, as there are fewer placesfor bacteria to grow, and there is no lubricant to be lost during thesterilization process. Thus, the wrist described can be used forminimally invasive surgery applications.

Each finger 318 a, 318 b is machined as a single piece, with the pulley18 a, 18 b that drives it. They are stainless steel with clearance holesdrilled in them, that ride on steel shafts made from drill rod. Thefriction torque is low because the shafts are only 0.047 in diameter.The shafts may also be titanium nitride coated stainless shafts, toavoid galling. The idler pulleys are made from teflon and simply haveclearance holes so that they ride smoothly on drill rod shafts. Becausethey are thin, and the alpha wrapped cable produces a moment on thepulleys, the pulleys must support themselves by leaning on each other.Despite the low coefficient of friction of teflon, this is still a majorsource of wrist friction. Because teflon is very soft, a teflon filleddelrin may be a better choice for this component. The main structuralwrist components are machined from 303 stainless steel.

Base Wrist Interface

FIG. 18 shows a view of the top of the wrist unit. This portion holds anumber of idler pulleys. The six cables shown in FIG. 16 that passthrough the instrument shaft 312 and the cable loop, which drives thewrist roll joint 3, about axis 3, shown in FIG. 17, all pretensionwithin this unit against various idler pulleys, some of which moveagainst screws to allow pretensioning. Six of the cable segments arealigned against the back of the wrist unit 374, such that they preciselyalign with the six drive cables Cb_(d2)-Cb_(d7) within the base unit,which run parallel to link 5. FIG. 18 shows these parallel cables,arranged, as shown, from right to left, as follows: Cw₂, Cw₇, Cw₆,Cw_(s), Cw₃; Cw₄. These six wrist cable segments are then mechanicallyfixed to their respective drive cables, for instance, using screwclamps, as shown in FIG. 13. The screw clamps are located roughly at thelocation of reference numeral Cw₆ in FIG. 18, for each cable. (Due tothe perspective in FIG. 18, the cables are not shown as preciselyparallel lines. However, they are, in fact, parallel.)

FIG. 19 shows the connection between the wrist unit and the base unit,simplified for a single degree of freedom. As can be seen from this sideview, the base drive cable returns around the pulley P7 and then onesegment Cb_(d) of the base drive cable passes adjacent to a portion ofthe wrist cable Cw. The other segment Cb_(r) of the base drive cable istensioned by the pulley P8 and passes near to the wrist cable Cw, butnot so near as the portion Cb_(d). The drive and wrist cablesrespectively are held together by the clamp 372. The wrist cable Cw isshown in FIG. 19 to be a loop, the other segment of which, Cw′, is shownon the opposite side of the wrist unit, not engaged by any other drivecables. For any given wrist cable, this may or may not be the case. Forinstance, the cable Cw₂, which rotates the entire wrist unit 304 aboutthe axis 3, is engaged by only one base drive cable Cb_(d2). However,the cable Cw_(s), which is connected to joints 5 and 7 in the wrist, isitself engaged to a drive cable. The cable Cw₅ is part of a continuousloop, of which the wrist cable Cw₄ is also a part. This wrist cable Cw₄is also connected to joints 5 and 7. It is also connected itself toanother of the base drive cables.

A generic set of attachments is shown in FIG. 13. The base drive cablesare shown in heavy line. Six continuous base loops are represented, eachdesignated Cb_(xn), where x is either d or r and n is 2, 3, 4, 5, 6 or7. The x component indicates whether the cable is a drive segment or areturn segment of the continuous base cable loop. The numerical ncomponent indicates to what motor the drive cable is coupled. Theindication “to P7 ₂” means that the cable goes to the pulley P7 that isassociated with the motor M2.

Because the cables in the wrist unit align parallel with the respectivecables in the base unit, no further mechanism is required to make anattachment other than a single small clamp per cable. In other words, nocomplex mechanical interlocking mechanism is required, and the actualconnection between the wrist unit and the base unit is frictionless.

Differential Kinematics

The relationships between the motor velocities and joint velocities forthe joints 2-7 are discussed next. The motor-joint mapping for joints 0and 1 are simply speed ratios. A matrix {dot over (q)} represents thevelocities of joints 2-7. All of the joint angles are measured withrespect to the previous link except joint 5, which is measured withrespect to the axis 2 of the instrument shaft 312. For instance, asshown in FIG. 14, the joint angle q₅ is −50°, 0°, and +90°, startingwith the uppermost configuration and going counterclockwise. A matrix crepresents the velocities of the six base drive cables that run parallelto link 5. R₃, R₄, R₅, and R₆ are speed ratios defined below for theembodiment described above.

R ₃=8.717×10⁻³ m/rad

R ₄=6.252×10⁻³ m/rad

R ₅=3.787×10⁻³ m/rad

R ₆=3.094×10⁻³ m/rad  (5)

We then have:

{dot over (q)}=Jċ,  (6)

where:

$\begin{matrix}{{J = {{{Rm}\begin{pmatrix}1 & 0 & 0 & 0 & 0 & 0 \\0 & \frac{1}{R_{3}} & 0 & 0 & 0 & 0 \\0 & 0 & \frac{1}{R_{4}} & 0 & 0 & 0 \\0 & 0 & 0 & \frac{1}{R_{5}} & 0 & 0 \\0 & 0 & 0 & 0 & \frac{1}{R_{6}} & 0 \\0 & 0 & 0 & 0 & 0 & \frac{2}{R_{6}}\end{pmatrix}}\begin{pmatrix}0 & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & 0 \\0 & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & {- 1} \\{- 1} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & \frac{1}{4} & 0 \\0 & {- \frac{1}{4}} & \frac{1}{4} & \frac{1}{4} & {- \frac{1}{4}} & 0 \\0 & {- \frac{1}{4}} & {- \frac{1}{4}} & \frac{1}{4} & \frac{1}{4} & 0 \\0 & {- \frac{1}{4}} & \frac{1}{4} & {- \frac{1}{4}} & \frac{1}{4} & 0\end{pmatrix}}},} & (7)\end{matrix}$

where Rm is a scalar which represents the ratio between motor rotationin radians to cable motion in meters.

The teleoperator slave of the invention discussed above has a number ofpositive features. The structure is stiff and strong. This results inlow flexibility, which provides good control performance and endpointmeasurement. The actuators are strong and well matched to the overallinertia, resulting in good positioning performance and grip strength, sothat needles may be securely held in a gripping end-effector. Thecarriage uses a bearing system that is rather stiff and low in friction.The first two axes of the system (0 and 1) are counterbalanced. Thisprovides safety and convenience, since the slave will not move whenmotor power is shutdown, which is particularly important if theend-effector is in a patient's body. The wrist unit 304 is detachable.This allows different wrist units to be used for different tasks, whileusing the same base unit 302. The five joint end effector allows forcereflection with respect to three translational DOFs. (This is discussedbelow.)

A brief discussion of the performance of the slave of the inventionfollows. Basic data, on a joint by joint basis, is given first, followedby tests to quantify force reflection performance. The ability toperform tasks is also confirmed, in particular, suturing and a moredifficult task of moving a piece of soft plastic tubing along a“S”-shaped curved wire.

Joint Limits

The range of motion of each of the slave joints is given relative to thezero position defined in FIG. 2.

q₀±800

q₁±600

q₂8 in(20 cm) stroke

q₃±180°

q₄−27°+40°

q₅±180°−q₄+30°−q₄

q₆±100°

q₇+200° jaw opening  (8)

Structural Stiffness

Estimates for the structural stiffness at the endpoint of the slavedescribed above is given below. These values are difficult to measureand are believed to be accurate to about 20%. Stiffness was calculatedby measuring the force required to deflect the instrument shaft by 1/16in (0.16 cm) in the x direction and ⅛ in (0.32 cm) in they directionusing a force gauge. The z direction structural stiffness is that foundfor the base unit.

k _(wx)≅9500 N/m

k _(wy)≅2800 N/m

k _(wz)≅12000 N/m  (9)

These measurements were made with the wrist unit centered in its stroke.The point where force was applied was 0.15 m (6 in) below the teflonsupport bushing 370, and 0.086 m (3.4 in) below the remote center 111.

Friction

The force required to backdrive each joint of the wrist with the basejoints 0 and 1 held stationary, and when the manipulator was in its zeroposition (FIG. 2) was measured. In each case four to six measurementswere made and averaged.

f_(R) is a force in the x direction applied in line with axis 5, whichcauses rotation about axis 3 only.

f_(x) is a force at the finger tips in the x direction with the fingersclosed. Axis 3 is held fixed, so only axis 6 may rotate.

f_(y) is a force at the finger tips in they direction. Only axis 5rotates.

f_(z) is a force at tip in z direction. Only axis 4 rotates.

f_(q2) is the force required to backdrive the carriage 310 and wristunit 304 together.

In the first case, these forces were measured with the 5 system turnedcompletely off.

f _(R)=0.63±0.04 N

f _(X)=1.1±0.2 N

f _(Y)=0.60±0.2 N

f _(Z)=0.96±0.06 N

f _(q2)=12.9±0.03 N  (10)

In the second case, a friction compensation algorithm was applied, whichwas used throughout the remainder of the results given. This algorithmwill not be described here in detail. It essentially feeds forward atorque to each motor as a function of motor velocity and includes amodel of the brush friction and brush flexibility. When the frictioncompensation algorithm is implemented, the measured friction values are:

f _(R)=0.48±0.01 N

f _(X)=0.88±0.14 N

f _(Y)=0.40±0.2 N

f _(Z)=0.73±0.07 N

f _(q2)=2.86±0.02 N  (11)

The friction is created in two places, within the wrist itself (cables,pulleys, etc.) and in the motors as brush friction. The fact that joint2 friction (fq2) can be reduced by a factor of four indicates that thisaxis is dominated by brush friction, because brush friction is the typeof friction for which the compensation algorithm compensates. However,in the other cases, where the compensation does not reduce overallfriction substantially, the friction must be in the mechanics of thewrist.

Master

A suitable master manipulator is a modified version of the PHANToM™brand haptic interface. Various models of such haptic interfaces areavailable from Sensable Technologies, Inc., of Cambridge, Mass. Such ahaptic master is described in U.S. Pat. No. 5,587,937, issued on Dec.24, 1996, and shown in perspective view in FIG. 20. The U.S. Pat. No.5,587,937 patent is hereby incorporated fully herein by reference. FIG.21 is a schematic showing the master kinematics.

The Cartesian axes of the master shown in FIG. 21 are aligned with thoseshown in FIG. 2 of the slave during use of the system such that mastermotions along its x axis cause slave motions along its x axis. Themaster is shown in its zero position. The system is essentially a threeDOF manipulator, which is approximately counterbalanced using the weightof its own motors. The standard PHANToM™ interface uses a passive threeDOF gimbal at the end of the actuated three DOF arm lm1, as shown in theabove referenced '937 patent. The gimbal has been replaced with aversion that uses panel mount optical encoders 374 with 256 counts/rev.(available from Bourns Inc., of Riverside, Calif., Model #ENS1JB28L00256) to measure the gimbal joint q_(M) 3, q_(M) 4, q_(M) 5,positions. A seventh joint between opposed interface elements 376 a and376 b was also incorporated q_(M) 6 into the last link of the gimbal tocontrol gripping motion of the slave manipulator. The master gripperuses a spring opening return so that the user can operate the opposedinterface elements 376 a and 376 b somewhat like a pair of tweezers.

The link lengths are:

l_(M)1=0.143 m

l_(M)2=0.178 m  (12)

and the speed ratios are:

R₀=9.970

R₁=9.936.

R₂=9.936  (13)

Each master motor is capable of producing 29.61 mNm(milli-Newton-meters) of maximum continuous torque. At two times maxrated continuous torque (which is typically how the system is run),maximum endpoint force values can be achieved of:

f_(MX)=4.1N

f_(MY)=4.1N.

f_(MZ)=3.3N  (14)

Each master motor encoder is a Hewlett-Packard optical encoder with 2000counts/revolution {after quadrature). This gives an endpoint measurementresolution of:

r _(x)=4.51×10⁻⁵ m(1.77×10⁻³ in)

r _(y)=5.63×10⁻⁵ m(2.22×10⁻³ in).

r _(z)=4.52×10⁻⁵ m(1.78×10⁻³ in)  (15)

A passive gripper does not allow the user to feel gripping forces, butit is relatively lightweight. An actuated gripper allows the userinterface to feel and to control gripping. If an actuated gripper isused in the master, the master must be modified to carry the weight ofsuch an actuated gripper. This can be done by adding appropriatecounterweight, and bigger motors and by counterbalancing the gimbalitself. The actuated gripper can consist of tweezer type implements asshown, or of a pair of standard type needle holder handles attached to asingle rotary axis. One handle is fixed to the gimbal end, while theother is attached via a cable transmission to a brushed D.C. electricmotor (such as Maxon RE025-055-035, graphite brushes). Of course, if theslave does not have an actuated end effector, such as if the endeffector is a saw, or a knife blade, then the master need not have anactuated user interface element.

Inertia

The inertias of each joint of the slave were calculated by plottingoscillatory step responses where very little damping and a known springconstant (position gain) were used. These were compared to a simulationof a spring, mass and damper system. The simulation mass and dampingwere modified until a fit was found to find the actual mass and damping.

I₀=0.32 kgm²

I₁=0.25 kgm²

I₂=3.35 kg

I ₃=26.0×10⁻⁶ kgm²

I ₄=20.0×10⁻⁶ kgm²

I ₅=20.5×10⁻⁶ kgm²

I ₆=19.5×10⁻⁶ kgm²

I ₇=2.8×10⁻⁶ kgm²  (16)

Individual Joint Responses

To give an idea of the position servo performance available with theinvention, individual joint responses are first shown for a fairly welltuned set of gains given below:

K _(qr0)=3500 Nm/rad

K _(qr1)=3500 Nm/rad

K _(qr2)=20000 N/m

K _(qr3)=1.5 Nm/rad

K _(qr4)=0.8 Nm/rad

K _(qr5)=0.3 Nm/rad

K _(qr6)=0.2 Nm/rad

K _(qr7)=0.05 Nm/rad  (16)

B _(q0)=35 Nms/rad

B _(q1)=35 Nms/rad

B _(q2)=200 Ns/m

B _(q3)=0.015 Nms/rad

B _(q4)=0.008 Nms/rad

B _(q5)=0.003 Nms/rad

B _(q6)=0.002 Nms/rad

B _(q7)=0.0005 Nms/rad  (17)

During master-slave operation, gains for joint 0 and 1 of much lowerthan 3500 were used, because the system was not stable at these highgains. This may have been due to limited position measurement resolutionin the master. A joint 0 gain of 3500 N/m corresponds to an endpointstiffness of 128,400 N/m, when the tip of the slave fingers are at adistance of 0.17m from the remote center. This is an extremely highendpoint stiffness. The endpoint resolution about joint 0 is the resultof a 4096 count encoder and a 137:1 speed reduction, which gives 561,152counts/rev or at 0.17m a 3.03×10⁻⁷ m resolution. The inertia of thisaxis is high, at 0.32 kgm², so that the bandwidth of the response isonly √{square root over (3500/0.32)}=104 rad/sec≅17 Hz. With such highpositioning resolution and inertia, such high stiffness is clearlyachievable. However, the master used had an endpoint resolution of only4.511×10⁻⁵ m. Therefore, if the slave tracks the master at this highgain, each time the master moves by one encoder tick, the slave sees aforce step of 5.8N or 1.3 lbs. Tracking such a coarse input createsnoticeable vibration in the system.

Also, the slave shows a structural flexibility at roughly 8-12 Hz. It isbelieved that the vibration caused by tracking the coarse master inputcombined with these structural dynamics caused instability at high gainsand forced detuning the slave joint 0 and 1 gains to 200 Nm/rad, whichcorresponds to an equivalent endpoint stiffness of 6920 N/m. One encodertick movement on the master corresponds to a 0.31 N(0.07 lb) force stepfor the slave.

Thus, the designer must keep these matters in mind.

The second reason the gains are different during the force reflectiontests is that they must be adjusted to have a 2:1 force scaling. For thetest, joint P.D. (position/derivative control gains were used (insteadof a cartesian P.D. mapped to joints via a J^(T) (Jacobian transpose)).

The joint gains must be set to give an endpoint gain which is ½ that ofthe master, or 240 N/m. These gains are dependent on the configurationof the wrist. For the force reflection tests, where the manipulator wasalways nominally in its zero position (FIG. 2) the gains given belowwere used:

K _(qs0)=200 Nm/rad

K _(qs1)=200 Nm/rad

K _(qs2)=20000 N/m

K _(qs3)=0.12 Nm/rad

K _(qs4)=0.10 Nm/rad

K _(qs5)=0.20 Nm/rad

K _(qs6)=0.10 Nm/rad

K _(qs7)=0.04 Nm/rad  (18)

B _(q0)=10 Nms/rad

B _(q1)=10 Nms/rad

B _(q2)=250 N/m

B _(q3)=0.004 Nms/rad

B _(q4)=0.003 Nms/rad

B _(q5)=0.004 Nms/rad

B _(q6)=0.003 Nms/rad

B _(q7)=0.0007 Nms/rad  (19)

Basic Teleoperator Controller Selection

Before consideration of the force reflecting capabilities of theinvention, a brief review of general control background is helpful. Auseful configuration for a master-slave system is where a ‘macro-micro’manipulator is used as the slave. As used herein, a “macro-micro”manipulator has a lightweight, short range, small manipulator mountedserially on a heavier, longer range, larger manipulator, which largermanipulator is kinematically closer to ground. In some of the followingdiscussion, the heavy manipulator is referred to as the proximalmanipulator, and the lightweight manipulator is referred to as a distalmanipulator. The macro and the micro manipulators are redundant, withrespect to translation in any direction, as defined above. It has beenfound that a Jacobian Inverse type controller enables achievingsatisfactorily scaled force reflection using a one-degree-of-freedomexperimental master-slave, macro-micro testbed and the three DOFembodiment of the invention shown in FIG. 1.

Basic Force Reflecting Teleoperation

Consider a master manipulator and a slave manipulator, each with its ownsensors, actuators, power supplies and amplifiers. Controlling eachmanipulator is a computer, which reads sensor values from each, andwhich commands actuator inputs (e.g. supply currents for an electric)based on a controller program operating on the computer. Using such asystem, a human operator can interact with the slave environment. In thecase of the present invention, this may be a surgeon interacting withtissues at the surgical site.

Only force feedback is considered here.

A Basic Teleoperator

The dynamics of a kinematically similar master and slave may beexpressed as

H _(m)(q _(m)){umlaut over (q)} _(m.) +C _(m)(q _(m) ,{dot over (q)}_(m)){dot over (q)} _(m) +G _(m)(Q _(m))=−τ_(m)  (20)

and

H _(s)(q _(s)){umlaut over (q)} _(s.) +C _(s)(q _(s) ,{dot over (q)}_(s)){dot over (q)} _(s) +G _(s)(Q _(s))=−τ_(s)  (21)

where q is the vector of joint positions, H is the inertia matrix (beinga function of the joint positions), C{dot over (q)} are coriolis torques(being a function of both the joint positions and the joint velocities),G are gravitational torques (being a function of the joint positions),and T are vectors of motor torques.

To control the system, gravity is compensated for by calculating andfeeding forward gravitational torques, and using P.D. (position andderivative) feedback to force tracking between the master and slavejoints.

τ_(m) =−G _(m))q _(m))+τ_(PD)

τ_(S) =−G _(s)(q _(m))−τ_(PD)

τ_(PD) =−K(q _(m) −q _(s))+B({dot over (q)} _(m) −{dot over (q)}_(s))  (22)

If the feedback gains K and B are symmetric positive definite matrices,the master and slave will appear to be connected via a spring anddamper.

Jacobian Transpose Cartesian Control

The basic controller discussed above assumes a kinematically similarmaster and slave. If this is not the case (as it is not with the masterand slave of the invention described above,) then the moststraightforward method of cartesian endpoint control is to implementtracking between the endpoints of the master and the slave manipulators.The endpoint position x and endpoint velocity {dot over (x)} arecalculated, based on the measured actuator positions and using themanipulator geometry. A P.D. (position and derivative) controller isthen applied to find the resulting endpoint forces and torques F forboth master and slave. These are then converted to joint torques τ forall of the joints and commanded to the master and slave motors.

Endpoint velocities are calculated as follows, where J is typicallyreferred to as the respective manipulator Jacobian:

{dot over (x)} _(m) =J _(m)(q _(m))q _(m)

{dot over (x)} _(s) =J _(s)(q _(s))q _(s)  (23)

The joint specific P.D. is replaced with a cartesian version:

F _(PD) =K(x _(m) −x _(s))+B({dot over (x)} _(m) −{dot over (x)} _(s))

F_(m)=F_(PD)

F_(s)=F_(PD)  (24)

The joint torques that are commanded to the motors to achieve desiredpositions/velocities are then calculated:

τ_(m) =J _(m) ^(T)(q _(m))F _(m) −G _(m)(q _(m))

τ_(s) =J _(s) ^(T)(q _(s))F _(s) −G _(s)(q _(s))

FIG. 22A shows such system in block diagram form (with the kinematictransformations included optional scaling factors discussed below).

Scaling

One way to change the user's perception of the environment is to scalepositions and forces between the master and the slave. Scaling may beintroduced into the above system to change the size of relative motionsand to amplify forces between the master and slave. This is done byintroducing the scale factors ρ_(F), as shown in FIG. 22.

Scaling affects the user's perception of the environment and of theteleoperator as follows:

If ρ_(F)>1, and ρp=1, then forces are scaled up from the slave to themaster. Velocities are one to one. The user feels an increasedslave/environment impedance. Objects in the environment feel stiffer andheavier. This makes transitions between freespace and contact feel morecrisp and noticeable. However, the friction and inertia of the slavewill also be amplified and felt by the user. As a result, theseundesirable elements will have to be very low in the slave if ρ_(F) isto be large. Conversely, the environment feels a reduced master/userimpedance. The environment will more easily backdrive the master andhuman operator.

If ρ_(F)<1, and ρ_(p)=1, then forces are scaled down from the slave tothe master. Velocities remain one to one, the situation is inverse ofthe previous case. As long as ρ_(F)>0, some level of force reflectionwill exist.

If ρ_(p)>1, and ρ_(F)=1, then positions are scaled up from the slave tothe master. Forces remain one to one. Motions made by the human operatorare reduced, making fine motions easier to perform. Steady state forcesare equal at the master and slave. Therefore, the user feels a decreasein slave/environment impedance. Transitions made between freespace andcontact feel softer and are more difficult to distinguish.

If n_(P)<1, and n_(F)=1, then positions are scaled down from the slaveto the master. Forces remain one to one. Fine motion control is moredifficult, since errors in the user's motions are amplified. But theslave/environment impedance increases as felt by the master/user so thatcontacts are easier to distinguish.

If ρ_(F)>1, and ρ_(p)=1/ρ_(F), then positions are scaled down from theslave to the master, but forces are scaled up in such a way that theenvironment stiffness appears unchanged to the user.

Macro-Micro Control

As mentioned above, it is beneficial to use a macro-micro manipulator asthe slave in a master-slave system. Referring to FIG. 23, the principlebehind the macro-micro control of positioning mechanism base 304 andwrist 302 is described. A “macro-micro” manipulator slave has alightweight manipulator, mounted on a heavier manipulator. The slave canhave a “sensitive” end effector (wrist and fingers), which islightweight. and low in friction, but with a small range of motion. Ifthis wrist is mounted on the end of a larger manipulator, withconsequently larger inertia and larger range of motion, it is possibleto suppress the reflected inertia of the macro manipulator, so that theuser who engages the master does not feel it, and to have an endpointimpedance that approaches that of the micro manipulator.

A high quality, force-reflecting teleoperation with force scaling of atleast 2:1 and perhaps 10:1 can be achieved, with the embodiment shown inFIG. 1, without the use of explicit force sensing. The controleffectively (a) hides much of the inertia of the slave manipulator fromthe user, at the master, who feels primarily the dynamics of the masterand that of the slave micro actuator end effector, and (b) thereforemakes the slave respond more readily to forces from the environment.

It is not desirable to reduce the inertia of the master as well. Eventhough the user feels both the inertia of the master and the slave,because of force scaling, the inherent symmetry of the system is broken.If master forces are magnified with respect to slave forces, then themaster must be able to achieve a proportionately higher servo stiffnessthan the slave. Reducing the inertia of the master reduces the servostiffness that the master can achieve. In this case, it is desirable tohave a master inertia larger than the slave, in direct proportion to theforce scale factor.

Macro-micro control, as defined here, is the use of two or moreredundant degrees-of-freedom (as defined above) actuated in series, viaan appropriate controller, one being a macro DOF and one being a microDOF, for the purpose of reducing the effective inertia, as measured fromthe distal side of the macro-micro system (e.g., the side that interactswith the patient in an MIS system) to approximate that of themicro-freedom, while retaining the range of motion of the macro-freedom.

FIG. 23 depicts an example of a one DOF master-slave system, thatillustrates the macro-micro concept, and upon which tests have beenconducted.

The slave 400 has two degrees of freedom, a macro 401 and a micro 402freedom. The master 403 has one degree of freedom. All three joints aredriven by brushed D.C. servomotors (Maxon Motors RE025-055-035EAA200A)411, 412 and 413. In the following discussion of the system, all jointforces and positions are scaled by link lengths implicitly, in order toavoid carrying these values through the calculations. Joint forces andpositions are labeled τ₁ and q₁ respectively, and have units of newtonsand meters. Inertias are also measured at the endpoint of each joint andhave units of kilograms.

The first joint position of the link 407 of the slave 400 is labeled q₁and the output force for this joint (force at the tip of the link (i.e.,the intersection of shafts 4040 and 406) is τ₁. This first joint isdriven by a low friction, one stage cable reduction with a ratio of13.87:1. The joint one encoder 409 is a Hewlett-Packard optical encoderwith 2000 counts per revolution after quadrature. The output resolutionis therefore 27,740 counts per revolution. At a link length of l₁=0.0635m (2.5 in), this gives an endpoint resolution of 1.44×10⁻⁵ m (5.66×10⁻⁴in).

The second joint 2 is mounted to the link 407 of the first joint 1 suchthat the joint 2 axis A₂ is orthogonal to and intersecting with the axisA₁ of joint 1. The second joint position is labeled q₂, and the outputforce of this second joint is labeled τ₂. Mounted to the shaft 404 ofthe joint 2 motor is a “T” shaped output end effector link 406. Thesecond joint is direct drive and uses a Canon laser encoder (TR-36) 414with 14,400 counts per revolution after quadrature. At a link length of12=0.025 m (1 in), this gives an endpoint resolution of 1.11×10⁻⁵m(4.36×10⁻⁴ in).

The master 403 is a single rotary joint whose position at a masterreference point, such as the user handle 408 is labeled q₃. The forcefor this master joint is r3. The master 403 is driven by a single stagecable reduction with a ratio of 10.67:1. The encoder 416 on this axis isa Hewlett-Packard optical encoder with 2000 counts per revolution afterquadrature, giving a total resolution of 21,340 counts per revolution.At a link length (the point 408 where the user holds the master) ofl₃=0.044 m (1.75 in), this gives an endpoint resolution of 1.29×10⁻⁵ m(5.1×10⁻⁴ in).

The inertia for joint 1, the macro axis, is 1.16 kg. The inertia ofjoint 2, the micro, is 0.006 kg, and the inertia for joint 3, themaster, is 1.53 kg. The friction in each axis was measured using adigital force sensor. The friction in joint 1, the macro, isapproximately 0.47 N; the friction in joint 2, the micro, is 0.02 N; andthe friction in joint 3, the master, is 0.54 N.

Torques are calculated based on control laws and are commanded from acomputer (Dell P.C., 166 MHz Pentium Processor) to 12-bit D/A boards(SensAble Technologies, Inc., Cambridge, Mass.) which in turn commandanalog voltages to PWM servo amplifiers, (Model 303, Copley Controls,Westwood, Mass.). The servo loops ran at approximately 6000-Hz for thedata discussed regarding this test device. Encoder counters are mountedon the same board as the D/A converters.

To understand the qualitative effect of macro-micro control, considerthat a small external force is applied to one end of the end effectorlink 406 of the micro actuator 404 by its environment, e.g., itencounters a fixed object. Because the micro actuator 402 has lowinertia, and presumably also low friction, it will deflect relative tothe macro actuator 401 with little resistance. This motion will betracked by the master actuator 403, i.e., it will move to replicate it.If the user is holding the master actuator at 408, he will feel a force,and the sensitivity with which he will feel forces increases as theinertia and friction of the micro actuator 402 decreases. The utility ofcoupling the macro actuator to the micro actuator is that the macroactuator 401 applied to the micro actuator 402 increases the total rangeof motion of the slave 400. Since the micro actuator end effector link406 can only move a short distance relative to the macro actuator link407, the macro actuator 401 provides a moving base for the microactuator 402, so that the combined slave system has both the sensitivityof the micro actuator 402 and the large range of motion of the macroactuator 401.

Jacobian Inverse Controller

A controller that suppresses the inertia of the macro actuator well is aJacobian Inverse controller.

A one DOF version of a Jacobian Inverse controller is given as follows.(The subscripts are as above. 1 is the large, macro manipulator. 2 isthe small, micro manipulator relative to the macro manipulator. 3 is themaster. S is the slave tip relative to ground.) The master is commandedto move the master reference point to follow the position of the tip ofthe end effector link of the slave manipulator:

τ₃ =−K ₃(q₃−X_(s))−B₃({dot over (q)} ₃ −{dot over (x)} _(s)),  (26)

where

x _(S) =q ₁ +q ₂.  (27)

The slave macro is commanded to follow the position of the master,without regard to the actual micro end effector link position:

τ₁ =−K ₁(q ₁ −q ₃)−B ₁({dot over (q)} ₁ −{dot over (q)} ₃)  (28)

In other words, the macro controller assumes that the slave micro endeffector link at zero, relative to the macro. Finally, the microactuator is commanded to keep the end effector link at zero:

τ₂ =−K ₂ q ₂ −B ₂ {dot over (q)} ₂.  (29)

For the 1 DOF example, the gains are then tuned to provide as stiff amaster and slave macro as possible and then the slave micro gains aretuned such that the total endpoint stiffness of the slave is the desiredscale factor, for instance 50, times less than that of the master inorder to provide scaled, e.g., 50:1, force reflection. Gains whichprovide this are:

K ₁=7000 N/m

K ₂=163.74 N/m

K ₃=8000 N/m  (30)

B ₁=55 Ns/m

B ₂=1.331 Ns/m

B ₃=65 Ns/m  (31)

The macro and micro stiffnesses k₁ and k₂ form springs in series, sothat:

(163.74×7000)/(7000+163.74)=160 N/m  (32)

The micro axis is decoupled from the macro axis. Regardless of theposition of the master reference point or macro axes, the micro jointsimply tries to keep the end effector link at its zero position.

A freespace step response test for this Jacobian Inverse controllershows good results. The master and macro respond to each other and cometogether in straightforward second order responses. Since the inertiaand gains of these axes are similar, they essentially mirror eachother's motions. The micro axis barely moves during the motion. Theresponse appears well behaved and stable.

A contact response test for this Jacobian Inverse controller also showsgood results. Initially the master and slave move together, with theslave moving towards an aluminum block. The slave hits the block and itsend effector tip position comes immediately to rest. The master actuatorreference point overshoots the slave end effector tip position due tothe masters finite servo stiffness, but quickly comes to rest. The slavemacro (base) comes to rest at the position of the master, assuming theend effector to be at zero. A roughly 0.25 mm offset between the masterand slave represents a constant force being applied to the user. Adifference in curves for the slave and the base represent the relativemotion between the micro and macro motions. While the micro stays incontact with the block, it deflects relative to the macro actuator.

This controller is well-behaved during contact and provides crispfeeling scaled force reflection. During freespace motions and duringcontact, the feel is very similar to that of a basic teleoperator thathas only a micro actuator. It has the important advantage however thatthe range of motion is equal to that of the macro actuator.

Regarding the inertia that the user feels when the system is movedthrough freespace, the user feels the inertia of the slave macro freedommultiplied by 8/7. Examination of equations 26 and 27, and consideringthat in freespace motion, there is no disturbance applied to q_(s), thenq₃=0. These equations are then identical to those for a basicteleoperator, that does not have the macro-micro feature. However, thegain scale is 8000/7000, so that if one could increase the gain of themacro freedom further, the macro freedom would feel lighter. So usingthis macro-micro approach, while moving through freespace, the userfeels the inertia of the master, 1.53 kg, plus 8/7 times the inertia ofthe macro base, or 1.33 kg. Had only the macro base been used as theslave and implemented 50:1 force scaling, a slave inertia of 50 timesits actual inertia, or 58.7 kg would have been felt.

Extension to Higher Degrees of Freedom

The 1DOF Jacobian Inverse controller just discussed can be extended to ahigher number of degrees of freedom. The general equations are givenbelow.

The translation of a reference point on an end effector link of thewrist kinematically after all of the joints (except for joint 7, whichonly actuates gripping) for instance the tip of the jaw 318 a, has onlythree possible translational degrees of freedom. Translation of thisreference point is redundantly controlled by motion of the combinationof the base joints and the wrist joints. For each of the three axes oftranslation of the tip of the jaw 318 a, a plurality of actuatorscontribute to translation of the point along that axis. For each suchaxis of translation under macro-micro control, there is at least onemicro joint and at least one macro joint distinct from the micro joint.In the embodiment of the invention shown in FIG. 2, the joints 0, 1, and2, constitute the macro actuator joints and the joints 3, 4, 5, 6 and 7constitute the micro actuator joints.

Taking for instance actuation in the z direction, the joints 0, 1 and 2can all constitute a macro actuator, depending on where in its workspacethe end effector is located. Similarly, the joints 3, 4, 5, 6 and 7could all constitute micro actuators.

Controlling the RDOF Slave with a 7 DOF Master

It is possible to control a slave having a number of DOFs X with amaster that is characterized by a number of DOFs Y, where Y is less thanX. For instance, in the embodiment discussed above, the slave unitlinkage is characterized by eight DOFs (seven DOFs of the end effectorfinger 318 a, plus gripping) and the master unit is characterized byseven DOFs (six DOFs of the master reference member 376 a, plusgripping). Extending the single DOF macro-micro concept and JacobianInverse Controller to a higher number of DOFs, as provided by thepresent invention, requires the consideration of several items.

There is significant coupling among the various DOFs. In particular, itis not possible to associate individual motors as macro-micro pairs.

The wrist mechanism, which provides the micro axes, is also used tocontrol orientation. This dual role implies that (a) the designer musttrade off orientation tracking between master and slave with themacro-micro feature, and (b) that torque feedback can not be provided tothe master (the torque signals are effectively used by the macro-microto enhance force feedback). Fortunately, many tasks, such as MIS tasks,can tolerate considerable orientation errors. Also torque feedback isnot helpful as contacts are typically single-point and dominated byforces.

To provide three macro-micro axes, the wrist design of the inventionshown in FIG. 12 uses two sequential pitch axes, leading to 8 DOFs. Thisimplies a single degree of redundancy with respect to position,orientation and grip of the slave, which the 7 DOF master can notcontrol. Instead it must be controlled automatically.

The following controller design, which will be understood with referenceto FIG. 22B provides the full DOF extension and addresses the aboveitems. Some of the following operations are omitted from FIG. 22B forsimplicity.

The master tip position x_(m), tip orientation R_(m) (measured as arotation matrix), translational velocity {dot over (x)}_(m), and angularvelocity ω_(m), are scaled and offset 502 before becoming slavecommands. (The rotation operations are not shown in FIG. 22B.)

X _(sd)=(x _(m) +x _(offset))/scale  (33)

x _(sd) ={dot over (x)} _(m)/scale  (34)

R_(sd)=R_(m)R_(offset)  (35)

ω_(sd)=ω_(m)  (36)

The slave actual R_(s) and desired R_(sd) rotation matrices areconverted into an angular error vector e_(s).

$\begin{matrix}{R_{s} = {R_{sd}^{T}R_{s}}} & (37) \\{e_{s} = {\frac{1}{2}{{R_{s}\begin{bmatrix}{R_{s\; 32} - R_{s\; 23}} \\{R_{s\; 13} - R_{s\; 31}} \\{R_{s\; 21} - R_{s\; 12}}\end{bmatrix}}.}}} & (38)\end{matrix}$

A slave tip reference velocity {dot over (x)}_(sr) (6 dimensional) isdefined to include both translation and orientation.

$\begin{matrix}{{\overset{.}{x}}_{sr} = {\begin{bmatrix}{\overset{.}{x}}_{sd} \\\omega_{sd}\end{bmatrix} - {{\lambda \begin{bmatrix}{x_{s} - x_{sd}} \\e_{sd}\end{bmatrix}}.}}} & (39)\end{matrix}$

This incorporates 508 any position errors into the velocity command in astable fashion, so the Jacobian inversion 504 given below can operateentirely in velocity space. A separate position command is no longerneeded (for the inversion process). For example, a system lagging behindwill see a higher velocity command and catch up, whereas a system thatis ahead will see a slower velocity command. The bandwidth k controls510 this position feedback and should be selected to roughly match theoverall system bandwidth.

This cartesian (tip) reference velocity is converted into joint space504 through the Jacobian inverse.

{dot over (q)} _(sr) =J(q _(s))⁻¹ {dot over (x)} _(sr),  (40)

where J(q_(s)) is the Jacobian of the slave manipulator relating thejoint velocities to tip velocities at the given joint configuration.This is computed via standard robotics tools. Note the tip velocity isassumed to be six dimensional, including translation and orientation.

The Jacobian inverse is computed via a numerical SVD (singular valuedecomposition).

The joint reference velocity is then decomposed 512 into a desired jointvelocity {dot over (q)}_(sd) q_(1d) and desired joint position q_(sd).

{dot over (q)} _(sd) ={dot over (q)} _(sr)+λ(q _(s) −q _(sd))+q_(null)α  (41)

q _(sd) =∫{dot over (q)} _(sd) dt·  (42)

This undoes the combination of 508 above and allows the subsequent P.D.controller 514 to operate on position and velocity separately as isstandard. (A single signal line is shown in FIG. 22B coming into theP.D. controller 514, for both {dot over (q)}_(ds) and q_(sd). However,this is for simplicity only in the figure. In fact, they are operatedupon separately.)

The null-space vector q_(null) 516 (the combination of joint moves thatdoes not cause any tip translation) of the slave at the current jointconfiguration may be computed during the SVD routine mentioned above.

Scaling and adding 520 the null-space vector to the desired velocityprovides control of the slave arm within the redundant DOF. Themagnitude value a determines the speed of motion inside this null spaceand is selected to minimize a cost function C(q). It is also limited 518to prevent undesirably fast motions.

$\begin{matrix}{a = {- {{sat}\left( {{q_{mull}^{T}\frac{\partial{C(q)}}{\partial q}},\alpha_{\max}} \right.}}} & (43)\end{matrix}$

A quadratic function with a diagonal weighting matrix W, is used, thoughany other cost function is also 5 acceptable.

$\begin{matrix}{{C(q)} = {\frac{1}{2}{\left( {q_{5} - q_{4} - q_{c}} \right).}}} & (44)\end{matrix}$

This quadratic function is minimized when (q₅−q₄−q_(c)) equals zero. Forinstance, FIG. 14 shows this cost function minimized when q_(c) is zero.Beneficial results have also been achieved setting q_(c) equal to 0.4and W=20.

The desired grip position and velocity are appended, which are feddirectly from the master grip, to the above computed desired jointposition and velocity. The desired joint positions can also be limitedto restrict the mechanism motion to within some desired region.

A joint torque τ_(s) is determined (with standard gravity compensation516) and applied to the slave mechanism 520 according to a P.D.controller 514

τ_(s) =−K _(s)(q _(s) −q _(sd))−B _(s)({dot over (q)} _(s) −{dot over(q)} _(sd)).  (45)

The gains K_(s) and B_(s) have to be positive definite with diagonalgains selected for simplicity.

The gains of this controller are determined to provide good behavior ofeach joint. Therefore, for the large inertia macro (base) joints, thegains are high. For the small inertia micro (wrist) joints, the gainsare low. The bandwidth and damping ratio of each joint should be roughlyidentical.

To provide feedback to the master 522, of interactions between the slave520 and its environment 524, the slave actual tip position and velocityare scaled and offset 526 inversely from the scale and offset of themaster reference position and velocity at step 502.

x _(md)=scale·x _(s) −x _(offset)  (46)

{dot over (x)} _(md)=scale·{dot over (x)} _(s).  (47)

The master torques are computed (with gravity compensation 528) via aJacobian transpose and Cartesian P.D. (tip) gains 532:

τ_(m) =J(q _(m))^(T)(−K _(m)(x _(m) −x _(md))−B _(m)({dot over (x)} _(m)−{dot over (x)} _(md)))  (48)

The exact macro-micro behavior is determined by the gain selection.Disturbances at the endpoint (tip) of the slave effector 520 causedeflection of the low-gain/lowweight wrist axes. This is sensed andreflected to the master 522. Should the user 534 accommodate thisfeedback And allow the master 522 to deflect, the slave base joints willbe commanded to move also. Thereby allowing a small disturbance to movethe heavy base and completing the macro-micro concept. The macro-microbehavior discussed above is achieved by setting the gains for the microjoints in the slave joint P.D. controller 514 to be relatively small ascompared to the gains for the macro joints, for example as shown abovein Eq. 18.

The level of force amplification is determined by the relative gainsbetween master and slave. The slave effector endpoint stiffness isdominated by the wrist axes and may be fairly low. The master referencepoint stiffness is typically higher, so that small disturbances at theslave appear amplified to the user.

Other candidates for control schemes, other than the Jacobian Inverse,are discussed below. These include a Modified Jacobian Inverse and aSimulated Force Sensor Controller.

Force Reflection

In this section force reflection for the Jacobian Inverse controller isdiscussed, as this gave good results. When implementing a master-slaveteleoperator with force reflection, there are several qualities whichdescribe the quality of force reflection:

Freespace motions of the system should feel free. The user who isoperating the master should feel the master and little else. They shouldnot feel as if they are “dragging” or “carrying” the slave along withthem. If no forces from the slave are sent to the master (forcereflection is turned off and the master is used only as a positioninginput), then this will be the case.

Contact should feel like contact. Forces between the slave manipulatorand its environment should be reproduced—at the master.

The system should be sensitive. The lowest level of force that can befelt should be as low a possible. How low depends on the task at hand.The ability to discriminate when contact occurs and how delicatelycontact occurs depends on this value.

Because the system is multi-dimensional, these properties should beequally good in all directions. There should not be preferentialdirections of motion caused by anisotropic friction or inertia becausethis may mislead the surgeon while they operate.

The foregoing discussion has focused on using the macro-micro controltechnique to control a slave, with a master. However, the macro-microcontrol is a good way of controlling forces between a manipulator andthings that it contacts in its environment, regardless of whether themanipulator is controlled as a slave by a master.

Freespace Responses

Using the Jacobian Inverse Controller discussed above, an 8.0 rad/sec, 2cm amplitude sinusoid was commanded to the slave of the invention shownin FIG. 1 as the desired motion and the resulting slave motion wasrecorded. (In other words, the slave was commanded by a virtual master.)

Also recorded was the force commanded to the master through thecontroller and the force measured (using slave motor commands(currents)) at the slave tip. The actual force at the slave tip is zerobecause the slave tip is not touching anything

Freespace response in the x and y directions are quite similar to eachother. There is a substantial amount of tracking error, which ispresented as a force of roughly 1.5 N to the master. The diminished basetracking and diminished freespace performance is a result of loweringthe base gains from a possible 3500 Nm/rad to 200 Nm/rad during thesetests to achieve stability.

At a peak acceleration of 1.28 m/s², one would expect a force of:

0.77 kg×1.28 m/s²=0.98 N.  (49)

The 1.5 N force observed is not surprising, considering that onlyinertial forces are considered in the above analysis.

The z axis free space tracking performance is considerably better, asshown in FIG. 24A. (The solid line represents the master; the dashedline, the slave.) In absolute terms, the tracking error is less. Thiscase differs from the x and y direction cases in that the error in the 2axis is due to the micro axis more than the macro axis. The macro axis(joint 2) was running at a high (20,000 N/m) gain which, unlike in thejoint 0 and 1, axes does not seem to cause vibration. This is likelybecause structural stiffness is higher in the z direction and theinertia being moved is considerably less.

Joint 4 acts as the micro axis during the z direction tests. It iscoupled to joint 2 (through the cable drive) such that when thedirection of motion of joint 2 changes, a force equivalent to the joint2 backdrive friction is introduced to the joint 4 and hence the output.This explains a cyclic sharp rise and fall in the output error plot whenthe direction of motion changes.

Contact Responses

During contact experiments the PHANToM™ haptic interface is used as themaster. The tests were made by moving the PHANToM™ master to control theslave such that the slave came into contact with a rigid aluminum block.Because the movement is done by hand, the tests are not entirelyrepeatable. But qualitatively, the responses look quite similar when thetests were run multiple times. A 2:1 force scaling was implemented.

Contact responses in the x and y directions look very similar. Fairlysubstantial freespace forces are shown, which one would expect from theresults of the previous tests. The contact is however, quite good. Asharp force increases in both the master and the slave, which closelymimic each other. The steady state forces settle to 0.5 N (slave) and1.0 N (master) showing the 2:1 force scaling which was implemented.

There is little overshoot seen in the measured slave tip position as itcontacts the aluminum block. This means the estimate of the endpointposition using joint measurements is good and shows that there isrelatively low structural flexibility.

The z direction contact is considerably better. This is in fact what onewould want all the responses to look like, as shown in FIGS. 25A and25B. The tracking performance, shown in FIG. 25A is excellent, asexpected with a 20000 N/m joint 2 gain. The resulting freespace forces,shown in FIG. 25B, are nearly zero. Then, when contact is made, a verysharp increase in force occurs in both the master and the slave, whichsettles to a steady state value of 0.7 N in the slave and 1.4 N in themaster as pressure is applied by the user.

This z axis is better than the others because the quality of each of themacro and micro freedoms involved is higher. The macro freedom, joint 2,has a backlash free transmission, is lightweight, and has excellentencoder resolution because four encoder signals are averaged indetermining its position. A gain of 20000 N/m means that inertia issuppressed by a factor of 20000/480=41.7. The joint 2 inertia is only3.35 kg, so that the user only feels 0.08 kg from the macro joint. Ifthe inertia of axes 0 and 1 could be reduced, the overall performance ofthe system might be improved.

Discrimination Tests

The lowest level of force that a user could discriminate correlates wellwith the wrist backdrive friction levels.

Representative System Test Tasks

Two tasks have been accomplished which show different aspects of thesystem. The first task was suturing. Suturing is primarily a geometrictask. That is, success depends on whether the system has sufficientdegrees of freedom, workspace, and the appropriate kinematics to makethe required motions.

The second test was a tube and wire test, where a piece of clear plastictubing was pushed along a wire bent into ‘S’ shaped curves. This taskrequires similar mobility to suturing, but also requires contact with amuch stiffer environment, namely a rigid metal wire. As a result, forcereflection becomes much more important because small motions can createlarge forces that are difficult to detect visually.

For the force reflection tests described above, a PHANToM™ Hapticinterface was used as a master. In order to perform these tasks and touse motion scaling, a larger master workspace was more convenient.Therefore, to demonstrate tasks such as suturing with motion scaling, alarger version of a PHANToM brand Haptic interface was used, known asthe Toothandle (described by Zilles, C. 1995 HAPTIC RENDERING WITH THETOOLHANDLE HAPTIC INTERFACE, Master's Thesis, Dept. of MechanicalEngineering, Massachusetts Institute of Technology). The Toolhandle isessentially a scaled up PHANTOM with 16 in. (40.6 cm.) link lengthsinstead of 5.5 in. (14 cm.) link lengths.

Suturing

To demonstrate the ability to suture along arbitrary suture lines,stitches were made in muscle tissue of an uncooked skinless chicken leg.An Ethicon Ethibond polyester suture (3-0) was used with a curved,tapered SH needle. A row of stitches could be made along different linesrelative to the instrument shaft. For example, one could suture along aline parallel with the instrument shaft, as can be done with difficulty(by some surgeons) using conventional MIS instruments.

Suturing was tried both with and without force reflection. With thesystem shown in FIG. 1, as described above, it was found that forcereflection is not always a help. If freespace motions do not feel freeenough, (for instance due to too much friction in the system) thenbackground forces cause fatigue during fine motions required forsuturing. Thus, the designer should consider reduction of any suchbackground forces.

A second reason that force reflection is not always beneficial is thatthere is a sufficient deadband in the forces that can be felt. Mostforces that are applied in suturing simply cannot be felt. Based ondiscrimination tests, forces below roughly 0.39 N to 0.58 N cannot befelt by a person using the device. To give an idea of how soft thetissue is, it was depressed with a force sensor (Mark 10 model BG) witha cone shaped attachment with a 60\deg included angle. To depress thecone approximately 6 mm required from 0.22N to 0.6N. Since one caneasily see deflections of less than 1 mm, one will see deflections andhence infer forces being applied, long before one can feel them withthis device.

Another way of stating this is that humans can already do this task (ofknowing when and how much contact has been made) fairly well visually.Whether or not very good force reflection is necessary for suturing isquestionable. It is unclear whether or not vision or touch is moreimportant during the suturing task even when performed during opensurgery.

Motion scaling used to reduce motions at the slave relative to themotions at the master makes fine slave motions easier, but reduces theenvironment compliance sensed by the user. It is already difficult tosense contact with soft tissue due to its low compliance. With anyfurther decreased compliance, due to motion scaling, sensing contactwould be essentially impossible. To compensate, one can implement forcescaling, which increases the compliance sensed by the user. However,some of the task forces are fairly large. For example, it can take asmuch as one or two lbs of force (4.4 N-8.8 N) to push our needle throughtissue. A similar amount of force might be used to draw a suturetightly. These forces, when scaled up-by a-factor of two, require twohands to apply while simultaneously controlling three positions, threeorientations, and a gripper. It is convenient to use the left hand tosupport the end of the master while using the right hand to control finemotions. Therefore, if force scaling is used to achieve satisfactorylevels of compliance, operation of the system as described above isdifficult with one hand and certainly operator fatigue arises.

Tube and Wire Test

Another qualitative demonstration is a task where a plastic (tygon) tubeis slid over a curved wire that is mounted in a small piece of wood. Thetube could be slid along easily when using bare fingers. This task issomewhat more difficult to accomplish using the invention than suturing,for several reasons. The required range of wrist motion is greater. Thecontact between the instrument and the wire is stiff. This means largeforces can be generated which cannot be resolved using visual feedback.Force reflection is therefore more important during this task thanduring the suturing task. Substantial torques can be applied to the wirethrough the gripper. However the system provides no torque feedback.Again large forces can be applied to the stiff contact without the userknowing. The grip force must be continuously modulated to successfullycomplete the task. With force reflection off, a test subject couldperform this task. However, it was necessary to watch the instrumentvery carefully for deflections in the instrument in order to determinebinding between the tubing and the wire.

With force reflection on, when the tube binds, forces are fed back,which stop the master from moving, so it becomes clear that the tube isstuck. However, because there is no torque feedback to tell the userwhich way to reorient the wrist to free the tube, one could only watchvery carefully and jiggle the tube in order to free it.

Given these observations on mobility and force feedback, for manyapplications, it would be beneficial to use the first wrist pitch (joint4) of the five DOF wrist primarily to avoid singularities, rather thanto achieve force reflection under macro-micro control. This would helpinsure that an output roll was always available, which is criticalduring suturing, while force reflection is not. However, for tasks otherthan suturing, and tube sliding, and for applications other than MIS,force feedback may be very useful.

Mechanical Design Considerations Base Unit

While each link of the base unit 302 described above was designed to bevery stiff, the bearings that connect them were not as stiff as might bedesired. The lowest structural natural frequency could be raised byincreasing rigidity. Larger bearings, appropriately preloaded, wouldincrease the overall stiffness. The spindle and Link 0 base bracket 308pieces could also be provided with increased rigidity. The spindleshould be stiff to resist torsional deflections about the x axis. Aredesign where the base motors (axes 0 and 1) use two stage cablereductions instead of a single stage cable reduction and a gearheadreduction may provide good results. The gearhead backlash may becontributing to an inability to raise base gains further during forcereflecting master-slave operation.

Wrist Unit

The wrist unit would perform some tasks better if it were, in general,stronger than described above. The full actuator potential of the basecan not be used with the wrist described, partially because it isundesirable to pretension the wrist more, due to the limited strength ofthe wrist unit and the Spectra™ plastic cable used. More pretensionwould require stainless steel, or better yet, tungsten wrist cable.Metal cable however, tends to preclude a non-alpha wrist design, due tothe extra friction created by alpha wraps when used with metallic cable.That would lead, then, to a bulkier wrist. It is critical that frictionin the wrist be reduced if macro-micro type controllers are to be usedfor implementing force reflection. Thus, the designer must balance theseconsiderations depending on the desired application.

Master

A few comments are warranted on the design of master manipulators forminimally invasive surgery, and in particular on the suitability of ahaptic interface similar to the PHANToM™ master for this purpose. Ingeneral, the PHANToM™ master is very good. It is athree-degree-of-freedom arm which is nearly counterbalanced mechanically(the remainder can be done in software using motor torques) and whichhas low friction and no backlash in the transmissions. There are severalareas to modify this device when used as a master manipulator with theslave of the invention. To have similar encoder resolution to the slave,resolution should be increased by roughly 100 times. This would give theslave a much smoother command to track. This would allow higher basegains to be implemented to improve both tracking and force reflectionperformance. Continuous force levels should be increased by about 10-20times to allow scaled force reflecting teleoperation. The structuralstiffness of the master is low and could easily be increased by severaltimes through modified design, especially through bearing design at thejoints.

A master wrist with more DOFs may also be desirable. While using thesystem, one often runs into rotational limits of the master well beforerunning into such limits on the slave. One solution is to use akinematically identical master and slave, so that singularities andjoint limits are aligned. However reorientation of the slave relative tothe patient would then require reorientation of the master to keep thisbenefit. Another solution is to increase the range of motion of themaster wrist, (i.e., the portion kinematically more distant from groundthan the link l_(M)2) most likely through the use of a four DOF wrist,that is through the addition of an output roll. In order to takeadvantage of this however, the master gimbal must have at least onecomputer controlled, powered joint (most likely the input roll (closestto ground)) in order to ensure that singularities are avoided. There isanother reason to power the master wrist joints when the device is usedfor MIS. When the surgeon lets go of the master (which happensfrequently), the master wrist will simply fall. Even if it werebalanced, one could bump it easily. The slave wrist will then track thismotion, potentially causing damage to tissue. Assuming that sensors areincorporated to determine whether or not the surgeon is holding themaster, then there are two options. First the master and slave can bedisconnected in software, so that when the master wrist falls, the slavewrist does not move. In this case, re-engaging the system may present aproblem. The surgeon would have to realign the two (with some sort ofvisual cues displayed on the video monitors for example) before thecontroller would re-engage the system. The second option is that themaster gimbal is powered so that when the surgeon lets go, it simplyfreezes in position so that misalignment between the master and slavenever occurs. Another advantage of this approach is that if the slavemanipulator is manually repositioned with respect to the patient, themaster manipulator can reposition and reorient itself automatically inorder to maintain visual correspondence between the two.

A disadvantage to powering the master wrist is that it generates asubstantial increase in design complexity and possibly weight. Finally,the designer may want to not only power the wrist, but design thesedegrees of freedom to allow precise application of forces in order togive the surgeon torque, as well as force, feedback.

Other Controller Candidates

The Jacobian Inverse controller discussed above worked well in themacro-micro context of the embodiment of the invention shown. However,other controller candidates were found to provide promising results, andshould be considered for embodiments and applications different fromthat shown above.

Modified Jacobian Inverse

One controller may be considered to be a Modified Jacobian InverseController. This method was originally developed to increase responsetimes of a slow and/or flexible industrial manipulator by adding asmall, high bandwidth micro manipulator to its end. See Sharon, A.,Hogan, N. and Hart, D. The macro/micro manipulator: An improvedarchitecture for robot control. Robotics and Computer IntegratedManufacturing, 10(3):209-222 (1993). The idea, which was used by for asingle manipulator, to command the micro actuator to null error betweenthe desired slave endpoint position and the actual slave endpointposition. If the micro actuator has a faster servo bandwidth than themacro actuator, then the micro actuator will tend to jump out ahead ofthe macro actuator and consequently decrease position response times.Its effect on a teleoperator system is discussed below.

The controller is given as follows. As in the Jacobian Inversecontroller, the master desired position is that of the slave tip:

Σ₃ =−K ₃(q ₃ −q ₁ −q ₂)−B ₃({dot over (q)} ₃ −{dot over (q)} ₁ −{dotover (q)} ₂)  (50)

Similarly, the macro desired position is equal to that of the master sothat:

τ₁ =−K ₁(q ₁ −q ₃)−B ₁({dot over (q)} ₁ −{dot over (q)} ₃)  (51)

In the Modified Jacobian Inverse method, the micro position is notservoed to zero, but rather directly to the master position:

Σ₂ =−K ₂(q ₂ −q ₃ +q ₁)−B ₂({dot over (q)} ₂ −{dot over (q)} ₃ +{dotover (q)} ₁)  (52)

This is what gives the jump out ahead behavior to the micro axis.

A representative set of gains is:

K ₁=7000N/m B ₁=55Ns/m

K ₂=160N/m B ₂=1.3 m

K ₂=8000N/m B ₃=65 Ns/m  (53)

Regarding both the step and contact response for this controller bothexhibit significant oscillation. The micro initially jumps out ahead ofthe macro axis. The overall amount of oscillation is greater due to theadded control input caused by the micro actuator. The overall speed ofresponse is roughly 10 times slower than in the Jacobian Inverse controlcase.

The increase in the level of oscillation in the system and poor contactresponse make this method of control less desirable than the InverseJacobian control for MIS. However, for other applications, or formanipulators with different kinematics and dynamics, this controller mayprove beneficial, and should be considered.

Simulated Force Sensor Controller

A known method to implement teleoperator force reflection is to use aforce sensor on the end of the slave manipulator and to feed theseforces directly back to the master. The master then tracks the endpointposition of the slave. It is possible to use the macro micro apparatusdescribed above using the micro actuator as a force sensor. In thiscase, the micro actuator is commanded to remain at zero:

τ₂ =−K ₂ q ₂.  (54)

This force is fed back to the master with a 50 times force scaling:

Σ₂=−50 τ₂.  (55)

The macro is commanded to track the master:

τ₁ =−K ₁(q ₁ −q ₂)−B ₁({dot over (q)} ₁ −{dot over (q)} ₂).  (56)

The gains were:

K ₁=7000 N/m B ₁=55 Ns/m

K ₂=163.74 N/m B ₂=1.331 Ns/m  (57)

In a free space test, because there is no contact being made with themicro actuator, no forces are commanded to the master. The micro alsodoes not move relative to the macro. The macro compensates entirely onits own and eventually reaches the master position in a classic secondorder response. In a contact test, when contacting a rigid surface, theslave displays a contact instability. Because the scaled contact forceis fed directly back to the master, the master is forced backwards awayfrom the contact block. The macro axis tracks this motion and pulls theentire slave away from the aluminum block at which point the forcecommanded to the master drops to zero. But the user is still pushing themaster towards the block, so the micro re-initiates contact. A violentincrease in the amplitude of the oscillations occurs.

As with the Modified Jacobian Inverse method, the behavior mentionedabove make this method of control less desirable than the InverseJacobian control for MIS. However, for other applications, or formanipulators with different kinematics and dynamics, this controller mayprove beneficial, and should be considered.

Improved Force Reflection

If the quality of force reflection needs to be improved, one option isto further improve the transmission characteristics of the slave,primarily to reduce friction. Brushless motor technology, whichtypically has had many problems when applied to force control, may haveimproved sufficiently to be of use.

Features

With a teleoperator master placed in the loop in addition to the slave,several features are possible. A few basic results are discussed below.

Alignment of Visual Image with Hand Motions

A basic feature is to orient the visual image of the surgical site andslave tip motions with those of the surgeon's hand and mastermanipulator. If the surgeon were directly viewing the operating site,master and slave motions could coincide in an absolute reference frame.But if the slave is viewed on a monitor, the reference frame of theslave must be rotated such that it coincides with the viewing directionof the camera. The reference frame of the master is rotated such that itcoincides with the reference frame of the monitor. Then a motion of themaster directly towards the monitor, for example, will be a motion ofthe slave directly away from the camera and the image of the instrumenttip on the monitor will coincide with motions of the master manipulator.In this way, motions made by the surgeon coincide with those that appearon the monitor.

Having high resolution 3-D vision is also important Humans rely onvision and without it, are at a loss. While this is not a focus of thisinvention, it will be important in a fully functional system for humansurgery.

It is also possible to project a stereo image of the surgical site tothe surgeon using a mirror. The system must be aligned very carefullysuch that the slave instrument tips appear (in the mirror) to extendfrom the tools that the user is actually holding with their hands, whichare partially visible from outside the sides of the mirror. This createsa powerful illusion.

Visual Overlays

Visual overlays can be included into the surgeon's monitor view of theoperating site. Since this view is already planned to be in 3D, it ispossible to have images, MRI images of tumors for example, directlyoverlaid onto this view.

Motion Scaling

Motion scaling can be implemented as discussed above. The slave iscommanded to track scaled versions of the master motions. Rotationalmotions are not scaled. It is typically desirable to allow large mastermotions to correspond to small slave motions, as this makes the slavemore steady, in that jerky master movements are made smaller and lessnoticeable. It also effectively increases the position resolution of themaster. Motion scaling ranging from 1:1 to 5:1 have been used. The valueto choose is task dependent. 5:1 might work well when the surgeon isperforming ½ inch slave motions, but is inconvenient if making 2 inchslave motions. For suturing, 2:1 motion scaling works well.

Indexing

Indexing is decoupling the master from the slave (via the controller),to reposition the master within its workspace. Indexing is analogous tolifting a computer mouse from its pad (decoupling it from the cursor)and moving it back to the center of the mouse pad. This isstraightforward to implement, and logical for positions. It does notmake help to index orientations, because if master and slaveorientations become misaligned, it becomes very difficult for thesurgeon to determine how master motions correspond to slave motions.Position indexing is especially helpful when large motion scalingfactors are used. Position indexing can be activated by pressing amechanical switch, by voice activation command that is communicated tothe controller, or by any other suitable means.

Heptic Overlays

Haptic overlays can also be provided onto the workspace of the mastermanipulator. The designer can place walls or funnels within theworkspace in order to guide the surgeon or to protect sensitive areasfrom accidental contact. The designer must take care with both thevisual and haptic overlays to accurately register the information to theactual anatomy. Displaying the information is relatively simple.

Beating Heart Surgery

Another enhanced mode of surgery is operating on moving tissue, e.g.,operating on a beating heart, to avoid the need for a heart lung machineand the trauma and risk associated with circulating blood through it.The motion of the heart can be measured, and then the slave can trackthis motion. In the reference frame of the slave, the heart is thusstill. The same thing can be done to the image of the heart, either byhaving the arm which holds a camera track the heart motion, or bynulling out motions in the image using the measured position of theheart. Then the illusion can be created for the surgeon that the heartis still, when it is in fact beating.

Care must be taken in measuring where the heart is. For the slave totrack this, information must be provided at least at servo rates, andpreferably at better than servo rates, so that noisy data may befiltered. It is necessary then to determine six DOF motion at, e.g.,2000 Hz. It will be difficult, if not impossible, to do this using avideo image, which typically supplies information at 30 or 60 Hz. Onepossibility is to use a small instrumented mechanical arm, whose end (asmall horseshoe shaped platform for example) is placed directly onto theheart. A serial or parallel linkage with optical encoders mounted at thejoints could measure six DOF motion at sampling rates in the kHz range.This arm would then measure the heart's motions precisely, at rateslimited only by computational speed.

CONCLUSIONS

There are several problems in current MIS. The surgeon is deprived ofthree-dimensional depth cues and must learn the appropriate geometricaltransformations to properly correlatA hand motions to tool tip motions.The surgeon's ability to orient the instrument tip is reduced. Theincision point/cannula restricts the motions of the instrument from sixDOF to four because it must enter through a point and be along a linefrom that point. As a result, the surgeon can no longer approach tissuefrom an arbitrary spot and angle and is often forced to use secondaryinstruments to manipulate the tissue in order to access it properly orto use additional incision sites. Suturing becomes particularlydifficult. The surgeon's ability to feel the instrument/tissueinteraction is nearly eliminated. The present invention is based on thepremise that despite surgeons' considerable skill and ability to workwithin the constraints of current MIS technology, the expansion ofminimally invasive medical practice remains limited by the lack ofdexterity with which surgeons can operate while using current MISinstruments.

A teleoperator slave of this invention has been described. Thiseight-degree-of-freedom arm is structurally stiff and strong with highactuator capacity. The system is counterbalanced for safety by placingall of its actuators at its base and using cable transmissions toactuate the wrist and gripper. This also allows the wrist unit to bedetachable to allow use of other wrist-units that perform otherfunctions, such as cutting, grasping tissue instead of needles, andcauterizing. This basic concept also allows the portion of theinstrument that enters the body to be sterilized. The wrist has enoughdegrees of freedom to allow macro-micro control in all three lineardegrees of freedom, with the goal of allowing forces to be felt equallywell in all three directions. A Jacobian Inverse Controller works wellwith the macro-micro slave. Also disclosed has been a method toimplement such control using a master that has fewer degrees of freedom(joints) than has the slave.

The foregoing discussion should be understood as illustrative and shouldnot be considered to be limiting in any sense. While this invention hasbeen particularly shown and described with references to preferredembodiments thereof, it will be understood by those skilled in the artthat various changes in form and details may be made therein withoutdeparting from the spirit and scope of the invention as defined by theclaims.

For instance, the transmissions in both the base and the end effector ofthe slave have been described as predominately cable systems. However,these systems may be gear, pneumatic, belt or any combination thereof.For instance, it might be beneficial to include a rigid member in thetransmission at the locus of connection between the transmission of thebase and the transmission of the end-effector, thereby facilitating aquick release connection.

The actuators have been described as electric motors. However they canbe any suitable actuators, such as hydraulic, pneumatic, magnetic, etc.In such a case, rather than measuring the motor current to determine itstorque, the appropriate through variable is measured—e.g.—current for amotor, fluid flow for a fluid actuator, etc.

Further, as described, six joints (2-7) are included in the removablewrist unit. However, it would be possible to transfer one or more ofthese joints to the base unit, thereby requiring fewer moving parts inthe interchangeable end-effector. For instance, translation along androtation around the long axes 2 and 3, respectively, could be achievedusing a transmission that is part of the base unit 302, rather than theend effector 304. This would limit, somewhat, adaptability, for instancein changing the instrument's stroke. However, it would also simplify andlighten the wrist unit 304.

1-4. (canceled)
 5. The apparatus of claim 5, said instrument furthercomprising a second end effector element movably coupled to said thirddistal joint, such that said first and second end effector elements aremovable relative to, and independently of, one another.
 6. The apparatusof claim 5, wherein said articulate arm comprises a remote center ofmotion mechanism having macro degrees of freedom of movement that areredundant with the degrees of freedom of movement of the instrumentaround said first, second and third distal joint axes.
 7. The apparatusof claim 5, wherein said input commands comprise the operator moving atleast one master control handle, wherein movement of said instrumentcorresponds to a scaled increment of said movement of said mastercontrol handle.
 8. The apparatus of claim 11, wherein the forcesexperienced by the instrument during a surgical procedure are reproducedat the master control handle to provide the operator with forcefeedback, wherein the reproduced forces at the master are scaledincrements of the forces experienced by the instrument.
 9. The apparatusof claim 12, wherein the reproduced forces are reproduced in threedegrees of freedom of movement of the master, corresponding to threedegrees of freedom of movement of the instrument.
 10. The apparatus ofclaim 12, wherein the reproduced forces at the master correspond to anamplification of the forces experienced by the instrument.
 11. Theapparatus of claim 5, wherein said slave articulate arm comprises aslave linkage having a number X of DOFs, X being at least 7, and whereinsaid master input linkage is characterized by a number Y of DOFs where Yis at least one fewer than X.
 12. The apparatus of claim 5, wherein saidslave articulate arm and instrument have a combined X degrees of freedomof movement, and said master input linkage has Y degrees of freedom ofmovement, wherein Y is at least one fewer than X, wherein saidcontroller is configured to resolve a redundancy in control due to thedifference between the X and Y degrees of freedom of movement byapplying a cost function to a range of possible joint configurations,each of which provides substantially the same location for the endeffector member.
 13. The apparatus of claim 16, wherein X comprises 7slave degrees of freedom of movement and Y comprises 6 master degrees offreedom of movement.
 14. The apparatus of claim 16, wherein X comprises8 slave degrees of freedom of movement and Y comprises 7 master degreesof freedom of movement.
 15. A robotic surgical system comprising: anarticulate robotic arm; and a robotic surgical instrument releasablycoupleable to a distal portion of said articulate arm, said instrumentcomprising: at least a first end effector element movably coupled to awrist portion, and a proximal portion coupled to an elongate shaft, saidproximal portion coupleable to said articulate arm, said elongate shafthaving a longitudinal axis and a distal end coupled to said wristportion, said wrist portion having at least two segments, each of saidsegments having a segment axis, said segments movably coupled togetherin such a way that at least one of said segment axes can be positionedsubstantially parallel to said longitudinal axis of said elongate shaft.16. The system of claim 26, wherein the end effector element is capableof traveling along an arcuate path while said at least one of saidsegment axes remains substantially parallel to said longitudinal axisand without said elongate shaft of said instrument translating along, orrotating about, said longitudinal axis.
 17. The instrument of claim 26,wherein said wrist segments and said end effector are operativelycoupled to a remote input control device, wherein an operatormanipulating the remote input device can cause the wrist segments andend effector to move relative to a surgical site. 19-25. (canceled)29-37. (canceled)